statinf2.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Expected values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "import pandas as pd\n",
    "import pickle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def r(n, r):  \n",
    "    enc = b'\\x80\\x03}q\\x00(K\\x01G@\\x0c\\x00\\x00\\x00\\x00\\x00\\x00K\\x02G@\\x11UL\\x98_\\x06\\xf7K\\x03G@\\x05Uf\\xcfA\\xf2\\x13K\\x04G@\\x0c\\x00\\x00\\x00\\x00\\x00\\x00K\\x05K\\x01K\\x07K\\x03K\\x08K\\x02K\\tK\\x01K\\nX\\x08\\x00\\x00\\x00nu/da/daq\\x01K\\x0bG@\\x0c\\x00\\x00\\x00\\x00\\x00\\x00K\\x0cG@.U\\x81\\x06$\\xdd/K\\rG@\\x07V\\x04\\x18\\x93t\\xbcK\\x0eK\\x01K\\x0fK\\x03K\\x10K\\x01K\\x11K\\x04u.'\n",
    "    d = pickle.loads(enc)\n",
    "    if d.get(n) is not None and d[n] == r: return True\n",
    "    return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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77WSt9F7y91Fuk8dzjrMkeUmtrmHQODAUgoHb+dOaZPKKygCIbN2UZ8a6tm/gDuIjW/LoMFtxkD+vO8aVfAf54b/9AxRcVcdB7V3fN3AH7frYm442vwC5aTUOf+PgG9aU1a38W/G7hN95WEAbUcFRLIpfZO2/k/gO5/LONdj9DRoGQyEYuJVtp66y4agtz/6r0+MIbNKw4S5P39udjpY0GPnF5fxlQw027/O74PBntv59f4OmLRtAQg0jn1HxCABlBbDx2WqHJWcns/zkcmv/dwm/o3VA64aQ0MrDvR6mZ2vlvVJqLuUve1zwwDJoVBgKwcBtVJgl//PNcWt/1oAIhsWENrgcTZv48Op0m9fRqkMXSMrItR9kNsO3Gs+cXlOhxwQaHF9/mKzJ63hiHZzfaTdESslr+16z9keEj2B89PiGktCKr8mXl4e9bE2Qt+vSLnZc2NHgctwuSCn59a9/TUxMDHFxcRw8eND5pHpiKAQDt/HF/nRrKuvAJj78dpzzeANPMTQmlHs1wW+vfHPcfoM5+Su4aPkD8/GHe1/Ga0QmQOwsW//bP9htMG9N38r+TBV/4yN8+O2g33qtqlj31t2Z3nW6tf/6/teNDWYPsWHDBk6fPs3p06dZvHgxTzzxhMfvaSgEA7dQUFLO65tsrpO/uLMLbYIC6ny9d99VrT78bnwPfC07zHvO5dhyHZUVw+YXbQMHPwEt61F8KeFd1erD3c8rxQRKUSV/Bago4b8dsOWtmdVtFtHBdSugDvDuxHd5d2L9ZP1l/C8J9FUmuZTcFFanrK7X9fREamoqPXr0YMGCBfTp04d58+axefNmhg0bRteuXdm7dy8ABQUFPProowwaNIh+/fqxZs0a6/wRI0bQv39/+vfvz05L2t6tW7cyatQoZs6cSY8ePZg3b55TD7g1a9bw8MMPI4Rg8ODB5ObmcunSJYdz6ouRy8jALby7/SxXr6s0z21b+PP4iM71ul53NywuOoc158HBnaxBaq9uOMHoHm3w2/NvyLNs3gaGqKyk9aGFG4Rt2VEppsogtc0vQo+JfHlmFan5qQA092vOE/H1e0vsHlp/WUObhvJon0d5K/EtAN469BYToicQ6BfoZGYteSHYvdezu3ZejR+lpKTwxRdfsHjxYgYNGsRnn33Gjh07WLt2Lf/zP//D6tWreeWVV7jrrrv48MMPremvx4wZQ5s2bdi0adNN6a8BDh06ZJf++qeffnKY/vrChQtERtrqi0VERHDhwgXat/dcWVZjhWBQbzLzi1m8/Yy1/8y93WnapHapGKry9deq1Zdf392VoAD13nM2q4CvdiSpfEWVjHoWAur54Mn4WrX6MuI3SkEB5KVxY9c/7SKDF8QuqPdG8tcnv+brk/WX9eHeD9MmUBUmyi7O5qPkj+p9Tb1Qmf7aZDI5TH/96quvEh8fz6hRo6zpr8vKynj88ceJjY1l1qxZHDtmc7+uTH9tMpms6a8BXnrppWprIVS3gvC0qdBQCAb15t/bzlBcpmzevdq3YEb/CCcznPP666rVl9bNmvDkaFuBmMJt/4ASS6W2kK4wYH79b3LiddXqS0CwUlAW/pP0PtdKrgHQoVkHHuz1YL1v8fqu13l9V/1lberblF/3+7W1v/TYUvJKan7rbkzoJf11REQE6enp1n5GRgYdOnRwy+9YEy6ZjIQQ44B/oCqmvS+lfLXK5yNRFdXigDlSyi8t50cDf9cM7WH5fLUQYglwJ1D5v2i+lDKxHr+LgRe4cr2Yz/bYfOefGdsNk4vpKRqKR4ZG8cGOc5Rcz2ZmxQaoFG/0711PT9FQDJgPO/9JQV46Hwfa/jx/0fcX1sAwvTCpyyQ+PPohZ/POUlBWwLLjy+xiFeqNA7OOt2mI9NeTJ0/mrbfeYs6cOezZs4fg4GCPmovAhRWCEMIHeBsYD/QC5gohelUZlgbMBz7TnpRS/iCljJdSxgN3AYXAd5ohv6383FAGjZPF285as4zGhgczursH6xvXkQA/H35+Zxce9d1AkCgCwBzaXbma6g0fPxjxNJ+3aE6ejzK7hTfrwMQuE70s2M2YhImFcQut/U+PfUp+ab6DGbcODZH+esKECXTu3JmYmBgef/xx/vWvf7n996iK0/TXQoghwAtSyrGW/rMAUsqbolIsb/3rKlcIVT5bCNwppZznbGxNGOmv9UXWjRKG//V7q7novYcHuqXOAdQu/bUrFOXnUPG33jRHJbzb0fdVhk9zkxtfbdJfu0BhcR7j/jOMa5aV1gttRjJj/NtuuXZt0l+7QoW5gqlrplo3vn8Z/0t+0fcXdb6ekf66/ng6/XU4kK7pZ1jO1ZY5wH+qnHtFCJEkhPi7EKLa9bAQYqEQYr8QYv/Vq1frcFsDT/Hej2ft9g7G9NTf6qCSpgffsyqDM+b2PHsihtJy58nkvMEXZ1ZblUH78nImH/0Oyoq8LFX1+Jh87FYJS48t5UZlrQeDRocrCqE6g3CtquoIIdoDsYC2JtyzqD2FQUBr4L+rmyulXCylHCilHBgWVosMlAYeJaeglKW7zlv7v767q1s9IJYuVc0tFOfDbtsb9pvl00jPK+Wrg04S37nKkKWquYGi8iI+Omrz2FmQm49fwRU4sMQt1186bSlLp7nri1WMjx5PxyAVx5Ffms9/TlR97zNoLLiiEDKASE0/ArhYy/vMBlZJKcsqT0gpL0lFCfARkFDLaxp4kU92pVJoqXXQo12QXVSwO4iMVM0tHPgIitUGZW7TSL42DwFg8fazmM1uqBjYLFI1N7A2ZS3ZxdkAtPVtztTrlrftnW9CRZmDma4RGRxJZLC7vliFr8mXx+Met/Y/Pf4pJRUlbr2HQcPgikLYB3QVQkQLIZqgTD/OC4DaM5cq5iLLqgGhXiunAkdreU0DL1FcVmG3OnhiVBe3exYtX65avakogz22yNyA0c8QGKCsk2ezCthy4kr973F+uWr1xCzNLD1ue3ufH7eQJs0sq+L8C6puQz1ZfnQ5y4+644u1577O99G+mfKAySnOYd2ZdU5mGOgRpwpBSlkOPIky9xwHVkgpk4UQLwkhJgMIIQYJITKAWcC7QojkyvlCiCjUCmNblUsvE0IcAY4AoUAtE8obeItVhy6QXaD8qzsEBzAh1v2ucO+8o1q9SV6tHqYAzcII6DeHBxJsaSre+/Fs/e9x+h3V6snW9K2cz1eKNsgviGk9ZsMg25s3u96EetZAf2f/O7yz3/1lMP1MfszrOc/a/+TYJ5ilPvdoDGrGpcA0KeV6KWU3KWUXKeUrlnPPSynXWo73SSkjpJTNpJQhUsremrmpUspwKe3/d0gp75JSxkop+0gpH5RSGjtRjQCzWfK+5iH6s2HR+PnoNL5RSvUQrSRhIfgFMH9YlDXH0d5zOTdnQvUSHyd/bD2e2X0mzfyawaDHwNeSE+rSYTj/k5ekc870rtOVzMDZvLNGJtRGiE7/kg30ytZTVzhztQCA5v6+3J/gXnu0W0ndoR6ioB6qAx8DoH1wUybG2VY17/3o/UIvR7OOcvCKyr7qK3x5oMcD6oNmodB3rm3gzre8IJ1rBDUJYkbXGdb+J8mfeFGaxs+yZcuIi4sjLi6OoUOHcvjwYY/f01AIBrXive22h+ecQZG0CNBZpK+WXZqHZ9+50CzE2l2gSb63/sglLuR6161T+/AcFz3Ovk7yYE3076kNkHW6ASWrHQ/2fBAfoQLq9lzew4mcGooTGTglOjqabdu2kZSUxHPPPcfChQudT6onhkIwcJmjF/LYdVZ5wPiYBD8bXvc0zB4n6zSc2mjrD/ml3cd9woMZ0lkpiAqzZMlP3lslXLpxie/O2wL4H+71sP2AsG7QbZytv8s9QWqeoH3z9tzb6V5rX2sGawzoKf310KFDadVK1SIfPHgwGRlucpN2gJH+2sBlPrakkQaYENue8JZNPXavL12OX6+BvYttx93GQ2jXm4YsGBFtVXCf70vnv+7pVrdyn8PrJ+zyk8upkMqFN6FdAj1DqonUHfKkTcElLYcxL9Sp3OeXs+v7xTrnkd6PsCF1AwAbUzfy9MCnCW1a+8p5sR/HOh9UR448cqTGz/SS/lrLBx98wPjxnq+SZ6wQDFwit7CUtYdt4Sfzh0Z59H6hoarViZIbkKjxch5cfSqF0d3bEBWicvhfLy5nbWJtw2ssBISqVgdKKkr46vRX1r7WU8eOqOHQto86LiuEw3UL/goNDCU00LNlTXuH9iY+LB6AcnO53e/XGNBL+utKfvjhBz744AP++te/evLXBgyFYOAiX+zPsCax692hBf07erYY/ZIlqtWJpOVQqkp5EtIVou+sdpjJJHhwcCdr/5Nd550u46vl7BLV6sB3qd9ZU1y3b9aeOyOqlxUhYNACW3/f+3ZlNl1lSeISliQuqYOkteP+Hvdbj1ecXNGoymzqJf01QFJSEgsWLGDNmjWEhIQ4HV9fDJORgVPMZsmne2yBaA8P6eTxQh2VymD+/FpOlBL2fWDrD1qgHqY1MGtAJK99d5LiMjPHLuVzMC2XAZ1a1e6elcqgc22Fhc9Pfm49nt19Nj4mB4WFYmfBpudVPYfsFDi3DbqMrtX9KpXB/Pjay1ob7u10L/+37//IKc4hszCTbRnbuLvj3bW6hiOzjrdpiPTXaWlpTJ8+naVLl9KtWzc3Sl8zxgrBwCnbT1/lfLZKDNciwJfJfeuS27CBSNsFVyxxkX6BED/X4fDgQD8m97UVHVm6K9VzslXhWPYxkq4mASqwa1rMNMcT/JtD/AO2/r73PShd/Wji04TpXadb+5+f+NzB6MZHQ6S/fumll8jOzmbRokXEx8czcKDTZKX1xmn6az1hpL/2Do8t2WdN8fDY8Giem1i1HIb7qXP66y8fhaMr1fGA+TDpH06nHL2Qx8Q3VRBVEx8TO5+9i9DmtShGU8f018//9DyrUlYBKvXDqyNedTID5T31luXBIEzw1BEIdr1CnbvTXzvi4o2LjP9qvDViee3UtUQHO/ZMM9Jf1x9Pp782uI1Jzynk+5O2fD9am7vuuJ4JxzRvWlqbuwP6hAfTz7InUlphZvm+dCcz6k9eSR7rz6239ud0n+PaxFDNnog0w3791jLu0LwDIyNGWvsrTq7wojQGrmAoBAOHfLY3zZo+Z0TXUKJDnS+BvcahT8BsyQgaORjaue62+JBG0X22J40Kd2RBdcDaM2utGUF7tO5B37C+rk9O0OQ3OvixW7Kgeoq53W0muzUpaygq12ddBwOFoRAMaqSswsyXB2zBMA25Oli/XjWXMZvhoCbP/6DHanW/CbHtaRWooq4v5BaxIyXL9cmj1qvmIlJKVp5aae3P7j67dpv03cZDkGXfo+AqnNzg8tT189azfl5tvtj6MbjDYCKDVHqT62XX2Xx+s9M5jcmMrTfq+90ZCsGgRr4/cYWr19VbbJsgf+7u0XAV0QIDVXOZc1sh1+IJFdASetbs110dAX4+TO9vs8V/vjfN9cm+gaq5yOGrhzmTdwaApr5NmRA9wfV7Afj4Qj9NvMJB16OBA/0CCfSrzRdbP0zCZLe5/OUpx4FxAQEBZGdnG0qhDkgpyc7OJiAgoM7XMNxODWpE+1CcNTAC3wbMalpZT3zRIsfjrBzQPBT7zgG/2v9RzBkUyQc7VAqLTccyybpR4trm8imLsN1cE3bladvqYEL0BGuG0FrR7yHY/hogIWUL5KZBy45Op/1rn5J10SBXv9j6MzVmKm8deosKWcHBKwc5m3eWzsGdqx0bERFBRkYGRrncuhEQEEBEhOtOBlUxFIJBtVzMLWLbKdsf5eyBDZvVdIVl/9ElhVCQBSe+sfX7P1Kne3ZtG8SATq04cP4a5WbJygMZ/PzOLs4nplmEdUEh3Ci9wbeptkqy2rfnWtGqk4pBOPM9IOHQMhj9rNNpK5KVrA2pEEKbhnJnxJ18n/49AKtOr+LpgU9XO9bPz4/oaB3nyLrFMUxGBtXyxf4MKvdVh8WE0ClEx5vJh/9j20yOGARt6+4WO2eQTfEt35fudtPF+nPrrRurXVt1JTa0Hvl6+muS4B36FMx1D4LyNDO62dJirz2zljIdb4TfzrikEIQQ44QQJ4UQKUKI31Xz+UghxEEhRLkQYmaVzyotzC1UAAAgAElEQVSEEImWtlZzPloIsUcIcVoIsdxSntNAB1SYJSv221wv5wxyborwGlLam4v6P1zzWBe4L649Qf5q4Xw2q4C953Lqdb2qaM1FM7rOqF/Ed/f7INCSziA/Q5mOdMqwDsOsKb1zinOsqwUDfeFUIQghfIC3gfFAL2CuEKLqK1gaMB/4rJpLFEkp4y1Nu9P3V+DvUsquwDWgdm4hBh5jR0qWtT5Aq0A/7u3d1ssSOSBtF2Rb6gM0aQ6962iCsRDYxJcp/WyRy5+7MSbhePZxjmWrZGdNTE2Y2Hli/S7o28S+eE4tNpcbGh+Tj10kdmNLeHe74MoKIQFIkVKelVKWAp8DU7QDLGUykwCXsm0J9Vp0F1DpcvAxMNVlqQ08ygrNQ3BG/wj8fR3k1/E2WlfT2JkqvUM90a6I1h+5RF6Re8wb2ofgPVH3EOwfXP+LavdLTm6AG1dqHutlpsVMQ6BWRLsu7uLijTpmlzXwGK4ohHBA+5qUYTnnKgFCiP1CiN1CiMqHfgiQK6WsTPdX4zWFEAst8/cbngeeJ7ewlE3HMq392YO8UyJz61YX0laU3IBja2z9fvUzF1XSJzyY3h1aqFuUm1mX5OTBNWar07QVJRUldpHJTvMWuUpYNxWEByArIMlxNPDW+VsbJG1FdbRv3p6hHYYCIJGsPXNz/h4D7+KKQqjOyFmbnbaOlhwaDwBvCCG61OaaUsrFUsqBUsqBYWFhtbitQV1Ye/gipRVqodc3IphubYO8LJEDjq2GMlXfmbAeEN7fbZeeOcDmuqcNzqsrW9O3kl+aD0B483AGtRtU72ta0cYkJC4DHfvwT4mxGRfWpKwx4g10hisKIQPQviZGAC6v9aSUFy0/zwJbgX5AFtBSCFHp9lqraxp4ji/22x5+MxvY1VTLa6+p5pBEzZZV/AMO01zXlinx4fj5qOsdSssl5cr1mgcff001B6xOWW09ntxlMibhRge/3tNUZleAK8fgUmKNQ1/b+Rqv7XT2xXqOuzreRZCfesnIuJHBgcwDXpPF4GZc+V+5D+hq8QpqAswBXFrrCSFaCSH8LcehwDDgmFSvBT8AlR5JjwBrqr+KQUNx4nI+Ry7kAdDE18TkuA5OZniOdetUq5Gcs3D+J3UsfCDufgeDa0/rZk24u4dtM/0LR6uEC+tUq4HMgkx2Xtxp7U/uUrsoaqf4B9lHZidW59uhWHdqHetOOfpiPYu/jz/jo22lILWK0sD7OFUIFjv/k8C3wHFghZQyWQjxkhBiMoAQYpAQIgOYBbwrhLAkpKcnsF8IcRilAF6VUlbWlPtv4DdCiBTUnoKmqomBN/hSszq4t1dbgi25fXSJtkRmzBgIauf2W8waaDMbrTp4gfKK2lcoA1h3dp01BfSgdoOICKp7JGmNaM1GR76A8hL338NNTI2x+Y98d/47CssKvSiNgRaXIpWllOuB9VXOPa853ocy+1SdtxOoNvLGYkJKqI2wBp6jrMLM6sQL1v4sL5qLnGI229cU7ldDHeJ6cme3MEKb+5N1o4Qr10v48XQWo2uZz0lKafcWrH0YupVOw1Xqitw0KLqmPI5669Nxr09oH7oEd+FM3hmKyov47vx3nvteDGqFEalsAMAPJ66QdUPVf23XIoDhMZ4txF4vUrdDnsXxrWlrlf3TA/j6mJje3+b8VpfN5aSsJFLzUwEI9A1kTMcx7hLPHpMJ+mqqqSUu88x93IAQwm5z2TAb6QdDIRgAsPKg7WE3vX84PibP1kx2RtOmqlWL1lwUO0sFaHkIrbfRpmOZ5BaW3jzIp6lq1bAmxbY1NjZqrGczjWrLhaZshuuXbxrS1K8pTf1q+mIbjomdJ+IjVHzLgcwDpF/3fFEiA+cYCsGAawWlfH/CFtA0Y4AHbNy1ZMMG1W6i5AYc1/g0OKmZXF+6tQ0iLkIFkJVWmFmXdOnmQaM3qFaFkooSNqZutPa1b8UeoVUURI1Qx9IMR25ONb1h3gY2zHO9foKnCAsMY1j4MGt/3VnvbXQb2DAUggHrki5SVqH8weMjW9IlrP7Rvh7j+NdQuQkZ1hPax3v8ljM0dRK+Oui62Whb+jaulyp31fDm4fRv4744iRrpqynFeVjfhe0ndZlkPf76zNdGTIIOMBSCASsP2jaTZ/SvTRC653j5ZdVuQruZ3HeOW2MPamJS3w74WkxoB9NyOZdVYD/gyMuqVeHrM1/brtFlUv0S2blKz8ngazEJZR6By0fsPn5528u8vK26L7bhGRUxyhqTkH49ncNXD3tZIgNDIdzmnLl6g8T0XAD8fAQTvRh7oGXLFtXsyMuAc9stHQFxsxtEltbNmjCqu827aFXVVULmFtU05BTnsOPCDmt/UudJNAgBLaCnJmlelVXClnNb2HJOH1lRA3wDuDfqXmvfSGXhfQyFcJuzSrM6GN29Da2a6TgLedIKrBlOOo+CFg2nvLQrp68OXcBsdmze2HBuA+WWVF3xYfF0bNGAKcS1ZqMjX0BFec1jvYzWbLQxdSMlFfqNn7gdMBTCbYzZLFl1yKYQtDWFdYeU9m+7fT27mVyVu3q2oUWACtvJuFbE/vPXHI6vai5qUKJHQXNLoN6NTDi7tWHvXwv6telHeHOlbK+XXmd7xnYnMww8iaEQbmP2puZY6x60DPRjdA8dJw+8eAiyTqpjv2b2ZpEGwN/Xh0l9bSsSR5vLZ3LPkJytgvX9TH6MjRrrcfns8PFVqcAr0e676AyTMNkpTMNs5F0MhXAbo32oTYrroKu6ByEhqlnRrg56TYEmDV/SU7uC+ibpEsVllpKV/iGqWdCuDkZFjnJP3YPaol1BnVgHxSrTakhgCCGBITVM8g7a/ZUdGTvIKXZvlToD1zEUwm1KcVkFG47YApem6cS7qJKVK1UDoKIMjtpKT9LXvYnsXKV/x5ZEhajAsusl5Ww+bqkbMWKlaoBZmvnm3DfWOQ22mVyVdn2grSVrTHmxNXZj5eyVrJy90sHEhqdji47Ehyn34XJZzsZzG53MMPAUhkK4Tdl8PJPrJWqzMTq0Gf0iW3pZIgec+R4Ks9Rxi3CIGukVMYQQTO1nU5yrNfsvlRzIPMDlAqVoW/q3ZHj48AaT7ya0ijNpuffkcAFtOdFvzn7jYKSBJzEUwm2K9mE2NT68YXzka8Gzz6oG2D/MYmeqvD1eYppGIWw9eZWcglJIfFY17CNux0WNw8/Hixlj+8zEWovq3I+Qd4FnNz/Ls5ufdTjNG4yNGouvSW3aJ2UlkZqX6l2BblMMhXAbkn2jhK0nbeVIp/bTR+yBll27VKM4H05o3hjdXPegtnQKaUb/jmo1VW6Wqrxm1i7I2kVxeTHfpX5nHTuxS8NufN9Ei/bQ+U5LR8KRL9iVsYtdGbu8KlZ1tAxoyYjwEda+1uxm0HAYCuE25Jsjlyi3+NEP6NSKTiENv0HrMse/VjZwgLZ9oG1v78oDTNNsLmvddrdlbONG2Q0AOgZ1JC40rsFluwmtAnVSb9nbaL2N1p1ZZ6Sy8AIuKQQhxDghxEkhRIoQ4nfVfD5SCHFQCFEuhJipOR8vhNglhEgWQiQJIe7XfLZECHFOCJFoaZ5PSmMA2D/EtDZxXZKk8S7y8uqgkomx7a2pLA6l5Vq9jbTmoomdJ+rDDNdzki2VxZVkKC1wPN6LjIwYaVde00hl0fA4VQhCCB/gbWA80AuYK4ToVWVYGjAfqFq7rxB4WErZGxgHvCGE0O5e/lZKGW9pNReCNXAb57IKOJSmSVUR297LEjmgvETZvgEQ9r71XqRVlVQWV2+UUmYuZ0eGLVXFfZ3v84ZoN+MfBD00shRcqXmsl/H38bdLZaF13zVoGFxZISQAKVLKs1LKUuBzwC6Pr5QyVUqZBJirnD8lpTxtOb4IXAF0HP1066PdTB6l41QVEREQ0ewc1lQV0SMbNFWFM7SFc47nteBCBdZUFX3D+jZsqgpnaFZWEYXXiAjS76pQ6220MXUjZRVlXpTm9sMVhRAOaKtXZFjO1QohRALQBDijOf2KxZT0dyGEf22vaVA7pJR2ZTKn6dhc9Omn8OnUx2wntPl5dMBdPdoQZEllsTDlKf6r2LavoH2o6YIud0GgqoD3aZng0/gFXhaoZvq37U/7ZmrVml+az/YLRiqLhsQVhVCdIbRWuz1CiPbAUuBnUsrKVcSzQA9gENAa+O8a5i4UQuwXQuy/evVqdUMMXORQei7ns1UtgaAAX+6qZX3gBuXyUcg8qo59A6CHvh6yAX4+3Gcxtwm/bFLyVaoKX+Hb8KkqnFE1lcWRL7wnixNMwmTEJHgRVxRCBqCtuB4BXHT1BkKIFsA3wB+llLsrz0spL0lFCfARyjR1E1LKxVLKgVLKgWFhhrWpPmjNRffFtifATz+pKqry1KLrPLXxL6rT4z6V1llnTIlXK6w/Rf6d/8+kKqkNDx9Oq4BW3hSreiypwp+imKeOfAKlhV4WqGa0+y/b0reRX5rvRWluL1xRCPuArkKIaCFEE2AO4FIGKsv4VcAnUsovqnzW3vJTAFOBo7UR3KB2lFWY+fqwTY9XPsx0idlM4mEfEi9bUi/oxLuoKndEt6ZdsD+9mp6jh1BJAu/ropPN5Kp06A8hMSRSQWJFMZzyfhnNmujSsgs9W/cEoNRcyubzm70s0e2DU4UgpSwHngS+BY4DK6SUyUKIl4QQkwGEEIOEEBnALOBdIUSyZfpsYCQwvxr30mVCiCPAESAU+LNbfzMDO7afusq1QrVB1z44gDuiW3tZIgec3wGVefEDQ5QNXIeYTILhvYsQQn2vPgQwKmKUd4WqCSEaVUyCdpVg1FtuOFyKQ5BSrpdSdpNSdpFSvmI597yUcq3leJ+UMkJK2UxKGWJxM0VK+amU0k/jWmp1L5VS3iWljJVS9pFSPiilvOGpX9LAPvZgSnw4JpMOfORrQpuqovd08Gb6Byf4BB2yHpfm9aGsXL9mOLt9hJTNUJDlPVmcMD56PCahHk/7Lu+z5ocy8CxGpPJtwPXiMjYdy7T29exdRFkRHNNYJHVqLgIoM5ex+4qtHGVJbjzfJmc6mOFlWndWcQkA5nJIXuVdeRzQJrANd7S7w9pff269F6W5fTAUwm3At8mZlJQr566e7VvQvV2QlyVywKmNUJJPt5AzdOtwBSIGeluiGtl9cTc5xTmcx59UcxAVhZ2rzYCqJ7q1jaVb5Z+93jOganJBGWajhsFQCLcB2ofUNB0msrMjSfkeLJ70/1j8yill+9YplQ+pFyvC+WPWDMDET2eyuJxX7F3BHLD4/lUsNlleCDL2QfYZxxO8yN0d7ybAJwCA09dOczLnpJcluvUxFMItzuW8Yn46o2zFQsDkvjo2FxXmwGlbttBKV0k9UlBWwPdp31v7vVuMAlTpZ603l+5oFgIx99j6Oo5JaObXjNEdR1v7RkyC5zEUwi3O2sMXqEwaObRLCO2CA7wrkCOSvwKz8thZ+P0yFj7bxcsC1cyWtC0UV6iVwOtNb/Bae5s9/isdm40Wfr2QhWXZthNJy0HHWUWrBqlVmCu8KM2tj6EQbnFWHbK9rU7Vc+wB2LlCnrrRn1OnvCiLE9adsdm0Y/396eh3AX9f9ed0/FI+Jy7rM5jqVPYpTplLwN8S6JdzFjL2e1coBwzpMITWAcpF+krRFfZl7vOyRLc2hkK4hTlxOZ/jl9SDyd/XxLg+7bwskQNyzkL6HnVs8oVm+o1Kv1J4hT2XlawCQUhAa3xNgnt6tbWOWaXjVQLCBL0m2/o63lz2M/kxLmqcta9VxAbux1AItzDah9K9vdsRFKBff/7KzWQAYsboOvZgw7kNmC0puRLaJdDER2WM1WZAXXPoImazfk0xdu68R1dCean3ZHGCtnDO5rTNFJUXeVGaWxtDIdyimM2SNRpzka69i6S0f0vVcewB2LtAaiNqR3QNo7Ulnfjl/GJ2n8u+aa5u6DQcWlgUWFEOnNnieLwX6R3Sm6gWUYDazN+avtWr8tzKGArhFmX32Wwu56tNz9bNmjCiq35NMFw4ADkW98cmQdB9PPHxEK/DGnqnr53mRM4JQBV0GdNpDLSKh1bx+PmYmBRnKzi06qD+zEbx7eKJbxcPJhPEzrJ9oGOzkRDCSGXRQBgK4RZFay6aFNcePx8d/1NrH0a9poBfU954A954w3si1YT2YTQqchRBTYJgwBuqYV+SdMPRy9bymnrhjXFv8MY4yxerXYmdWA/Fed4RygW0CuGnCz+RU5zjRWluXXT8lDCoK0WlFWw4asv9oi0KrzsqypQNu5K++jUXmaXZzhd+UudJN42Jj2xJdGgzAG6UlNulDNEdbXtBO0tG2YoSOLbGu/I4IDIokn5t+gFQISvYcE6/2VobM4ZCuAX57thlbpSoco7Roc3oGxHsZYkckLIZCi229hbhyrYNPPiganpi3+V9ZBaqB3wr/1YMDR+qPtj5oGoo84bWvVdv3kYPfvUgD36l+WLjNJXoDuvXbAT2MQlGvWXPYCiEWxDtQ2h6v3CEjtM/cPg/tuO42cq2DWRkqKYn1p6xJd0bHz0eP5PFE6owQzUL2uSB205d5er1kgaT0RkZ+Rlk5Gu+2NiZyg0VVNrxa+e9I5gLjI0aa/3Ok7OTOZt71ssS3XoYCuEW48r1YrafspUanarnzKZF1+CkZukfp6+6yVoKywrZdH6TtT+5y+Qax3YMCSQhSgVTVZgla/WcyiKonX29iSP6rZMQ7B/MqMhR1v7XZ41VgrsxFMItxtrEi1S6vydEtyaydaB3BXJE8iqosPi/t4+HNj28K48DtqRtsfq/RwdH0yukl8Px0zQxCV8d1NlSpyp959qOD3/eaFJZrDu7zhoPYuAeXFIIQohxQoiTQogUIcTvqvl8pBDioBCiXAgxs8pnjwghTlvaI5rzA4QQRyzX/KfQtV2j8fCVxtVxRn8drw7A3matfSjpEK130eQuk52a4SbEtqeJJZVF8sV8Tl6+7lH56kX3CcrdFyA7RbkB65QR4SNo6d8SgMsFl9l/Wb9pNxojThWCEMIHeBsYD/QC5gohqr4epQHzgc+qzG0N/Am4A0gA/iSEqKxA/g6wEOhqaeMwqBfHL+VzTJOqYnxseyczvEjOWUjfrY5NvtBnht3HQ4aopgcyCzLZfUnJKhDcF12lbnLoENU0BDf1s0tl8dUhfawShkQMYUhElS+2SaBy963k8OcNK1Qt8PPxY3z0eGtfu69jUH9cWSEkAClSyrNSylLgc2CKdoCUMlVKmQRUXb+NBTZJKXOklNeATcA4IUR7oIWUcpeUUgKfAFPr+8vc7lRNVdFCz6kqtKuDmDHQ3D5w7i9/UU0PrD+33mqaGNRuEO2bV1G08X9RrQrTNfs3qw9doEIHqSz+MuYv/GVMNV9sX83+zdEvdZ3KQrt/s+n8JiOVhRtxRSGEA+mafoblnCvUNDfcclyXaxpUQ4VZ2hXCma7nzWQpIUnzFtpXv5vJUkq7zUttXh1njOwWRogllUVmfgk7z+i3hjGdhkFwpDouumZfl0JnaFNZFJYXsiVNv2k3GhuuKITqjKWuvurUNNflawohFgoh9gsh9l+9erW6IQbAj6evcsXi3hjavAkjuoZ6WSIHpO2Ca6nq2D8Yuo2/aciMGap5m+M5xzl97TQAAT4B3NPpnpsH/ThDtSr4+ZiYHG/LIbXygPfNRjNWzGDGimq+WJPJPnJZ6w6sM4QQdquEtSmG2chduKIQMoBITT8CcNWPrqa5GZZjp9eUUi6WUg6UUg4MC9NxPh4v8+UBez94Xz2nqkhcZjvuMx38bi7ak52tmrdZk2KL3h3TaQzN/JrdPKgkW7VqmKGJEt+YfJn84jK3y1gbsguzyS6s4YvVbuyf2ggF+l3RTOoyCWF5r9x9aTeXCy47mWHgCq48NfYBXYUQ0UKIJsAcwFWV/C1wrxCilWUz+V7gWynlJeC6EGKwxbvoYUC/cfM6J6+wjO80KRJmDNBxqorSAkhebevHz/OeLE4orSjlm3O2VBVTYqY4GF09vTu0oEc75cFTXGZmfdIlt8nndkJjIPIOdWwu13V5zXbN2jG4/WAAJNKIXHYTThWClLIceBL1cD8OrJBSJgshXhJCTAYQQgwSQmQAs4B3hRDJlrk5wMsopbIPeMlyDuAJ4H0gBTgDGMlJ6sjXSRcpLVebnn3CW9CjXQsvS+SA419D6Q11HNIVIgZ6Vx4HbM/YTl6JSvjWrlk7Etol1PoaQghmahT0lzowGzkk/gHbsXYlp0O0CnrNmTVIHcdPNBZcsitIKddLKbtJKbtIKV+xnHteSrnWcrxPShkhpWwmpQyRUvbWzP1QShljaR9pzu+XUvaxXPNJafxr1pmVmsCnmXpOZAeQqPFMjn8AdBx+ojUXTe4yGZOomxluar9wfE3q99x//hrnsgrcIp9H6D0NfC0mvMtH4FKSd+VxwF0d76K5X3MAzuef5/DVw16WqPGjY0OzgSukXLnBobRcAPx8BJP1XDc5Nw3ObVfHwuTQu+juu1XzFllFWfx44Udrf0oXB+aitnerVgOhzf0Z1b2Nte/NzeW7o+/m7mgHX2xAMPTUeFLpeHO5qW9TxkaNtfbXnDGszvXFUAiNHO3q4O4eba0Vu3TJ4eVYnck6j4YWNVdxe+451bzF+rPrqZCqlkH/Nv3p2KJjzYNjn1PNAVqz0VcHM7xWXvO5O5/juTudfLFas1HScl3HJEyNsYUvbTy3keLyYi9K0/gxFEIjpsIs7fLkzNTzZrKUcLiKuUinSClZfca28V2XzeSq3NWjDa0CVaDgxbxidp7RgQtVTUTfCUEWZV2YreuYhL5hfenUohMAN8puGDEJ9cRQCI2Y7aeukplviz24s7uO3XLP71TpKkDFHvS4z+Hw8eNV8wbHso/ZxR7c2+lexxN+GK+aA5r4mpiiMeet2J/uYLTnGL9sPOOXOfliTT725jwdby4LIezMeatSVnlRmsaPoRAaMcv32R4q0/qF67tM5qGltuPYmeDX1OHwoiLVvMFXp7+yHt/T6R6aN2nueEJFkWpOmDXQPiYhr7DhYxKKyoooKnPhi+2nKaJz6lu4rl8//0ldJlk3/Pdc2kPGdZ17cukYHT9BDByRdaOEzcdtsQf3D4p0MNrLFOfZxx70f8h7sjihqLyI9efWW/vTuk5z27V7dwimT7hyCS4tN7M6UV/V1OwI6aLSWQDICl1vLrdr1o6hHYZa+6tTVjsYbeAIQyE0UlYdvEC5ZWOyf8eWxLQJ8rJEDjjyJVQmIGsbq2of6JTN5zdzo0zFSXQM6sjAtu6Nk7h/oE1xa1d4uqSfRnEf+lTXdRKmd51uPV6dspoKc4UXpWm8GAqhESKlZLnGBj1nkAMPGD2gNRf1f0jXsQdac9G0rtPcXn50cnw4/pY6Cccu5XP0Qp5br+9Wek0Bf0uQY3aKykGlU0ZFjKJ1gKpSl1mYya5L+pVVzxgKoRFyMC2XlCvqLbZZEx/ui9Nx3YPLR+HiIXXs0wRiZ7k0beJE1RqStPw09meqgismYXJYJtOO8ImquUBwUz/G92ln7Tf0KmFit4lM7ObiF9sk0L5OxcGlNY/1Mn4+fnbV1LSK3cB1DIXQCFmheYhMjOtAM39fL0rjBO3qoMdECGzt0rRnnlGtIdF6qIwMH0mbwDYORmvo+YxqLnK/ZkW3OvECxWUNZ954ZugzPDO0Fl+sdr/n2Goozne/UG5Cazb6If0HcopzHIw2qA5DITQyCkrKWZdkSww7W8+byeUlKrCpEh1vJpeby+3SKLtzM7kqgzu3plOIqnV9vbicjUf168FDh/7QxpKJpqwQjq70rjwO6NKyC3FhcYD69zQS3tUeQyE0MtYevkhBqXqjjGnTnP4dW3pZIgccW6uKrQAEd4ToUS5PHTVKtYZie8Z2rhRdASAkIIQRESNcn7x5lGouIoRgtmZz+bO9aa7fq56MWjKKUUtGuT5BCHtFfmCJu0VyK9NjbKuEL099aSS8qyWGQmhkfLbH9vCYm9DR7ZuebuXAR7bj/g+rIiw65YtTtlTPU2Om4mfybPnRmQMi8LEkvNt7LoeUK9c9er96EXc/+Pir40uJcOGgd+VxwPjo8daaFan5qdY9IQPX0O9fqMFNHMnI44jFK6WJr4kZ/XWcyO7KCTj/kzoWPvaBTjrjwo0L/HRBySoQzOjm+VJtbVsEcE/Pttb+Z3t07IIa2FplQa1Eq+h1RqBfIPdF26LgtYrewDmGQmhEfLb3vPV4Ymx7WgbqOJGd1rTQYwK00K8n1MpTK5GWpHtDOwwlMqhh9mUeuMO2ubzyYEaDbi7XmoE/sx0fWanrzeVZ3W2ebJvPb+Za8TUvStO4MBRCI+F6cRlrEm2bydqHie4oK7JPZDfgZzWP9TJl5jI776JZ3Vxzi3UHw2NC6dhabS7nFZWx/oiOq6lF3gFhPdVxWQEcWeFdeRzQo3UPYkNjAfXvq61rYeAYlxSCEGKcEOKkECJFCPG7aj73F0Ist3y+RwgRZTk/TwiRqGlmIUS85bOtlmtWfuaij9/tyerEixRaNpO7tW3OgE6tvCyRA5JXq3QVAK2iVKrrWjJ7tmqeZlv6NrKKVO3gsKZhjIwcWfuLdJytWi0xmQRzEjSby3s8v7k8u/dsZveuwxcrhP0qYf8SXUcuaxX7l6eNzWVXcaoQhBA+wNvAeKAXMFcI0avKsMeAa1LKGODvwF8BpJTLpJTxUsp44CEgVUqZqJk3r/JzKeUVN/w+tyRSSruHxQONajP5kTptJi9apJqnWXHS9qY7reu0um0md1ukWh2YNSDSrpraycue3VxeNGgRiwbV8YuNux98LUkJM4/AhQPuE8zNjIseR5CfSudyPv88ey/v9bJEjQNX/lITgBQp5VkpZSnwOVA1QfwU4GPL8ZfA3eLmJ9ZcQL8ZsnTMofRcjl9SNtsAPxPT9Fwm8/JRSN+jjk2+dd5MLixUzSyr+LQAACAASURBVJOk56dbUxwIBDO61nEzubxQtToQFuTP2N62yOVle847GF1/CssKKSyr4xfbtKV95PK+D9wjlAdo6tuUiV1skctaxW9QM64ohHBA6wKRYTlX7RgpZTmQB4RUGXM/NyuEjyzmoueqUSAGFj7ZmWo9nhTXgeCmnnWJrBf73rMd95wEzetmCZwwQTVP8vnJz63Hw8OH06F5zRXcHLJ1gmp1ZJ52c/lABteLPZcWe8KyCUxYVo8vduCjtuOjK6FAv4V+Znezmca2pG0hsyDTwWgDcE0hVPegrmqQczhGCHEHUCilPKr5fJ6UMhYYYWnVhrEKIRYKIfYLIfZfvXrVBXFvLa5eL+EbzWbjI0OjvCeMM4quQZLmTSxhofdkcUJhWaHdZvLcHnO9JsuQLiHEtFE1FwpKK/jqoI7TYof3hw791HFFCRz6xLvyOCCmVQyD2g0CoEJWGC6oLuCKQsgAtH54EcDFmsYIIXyBYECbSGQOVVYHUsoLlp/Xgc9QpqmbkFIullIOlFIODAvTcUUwD/H53jTKKmxprvuEB3tZIgckfqbSGwC07QMdh3hXHgd8c+4brpcqe33HoI4MCx/mNVmEEDwypJO1//GuVP1uggphr+j3fQA6TjWtVfRfnPqC0gr91ofWA64ohH1AVyFEtBCiCerhvrbKmLXAI5bjmcD30vI/WghhAmah9h6wnPMVQoRajv2AicBRDOwoqzCzTLOZrOvVgdkMezXmooSFuk1zLaXkPyds7ydzesyxVtzyFtP6R9DckqTw7NUCfkrRrymG3tMh0GIRzkuHUxu9K48DRkeOpm2gCgDMKc5h0/lNXpZI3zj9K7DsCTwJfAscB1ZIKZOFEC8JISrzA38AhAghUoDfAFrX1JFAhpTyrOacP/CtECIJSAQuAJqniQHAd8mZXM4vBiC0uT/j++g3uIszW+DaOXUcEOxymmtvcCDzgLVmclPfpkyJqeoj0fA09/dl5gCbs8ASzb6R7vALUN5jlexd7D1ZnOBr8mV2d9tewmcnPnMw2sClvMlSyvXA+irnntccF6NWAdXN3QoMrnKuABhQS1lvOz7elWo9fiAhkia+Oo4j3POu7bjfQyqXfj2YP79+4jhCuzqY2HkiLZq0qN8FO8+v33wLDw3pZFUEW05kkp5TSGTr+n2PVZkfP989Fxr4KPz0BkgznN0KV09CWHf3XNvNzOg6g38f/jdl5jKSriaRnJVM79De3hZLl+j4CXN7c/xSPnvPqW0YX5Ng3uBOTmZ4kewzkFK5FBcw6LF6X3L+fM8ohcsFl9mStsXad8tmcuf5blEKXcKaM6JrKKBivj7d7X4X1Pnx892jFFpGQneNt5KOVwkhTUMYGzXW2jdWCTVjKASd8sGOc9bjsb3b0bZFgBelccLud2zHXe+F1p3rfcmsLNXczX9O/IcKqTZBB7YdSNdWXet/0eIs1dzAI0OirMef7U2joKTcLdetJKswi6xCN32x2s3lxM+gUL8FabSKf/259VwtvP08Fl3BUAg65Ep+MWsSba6Hjw6P9qI0TijMgcRltv4Q94QXz5ypmjspLCu0cz18qJebCvbsmKmaGxjdow1RmuI5X+x3bxbUmStmMnOFm77Y6JHKmwyUd5mOayXEhcXZFc/RxqAY2DAUgg75ZNd5O1dTXectOrDE3tU0+k6viuOIVSmr7FxNR0WO8q5A1eBjEjymeQH48KdUKsw6dkEd8ktbf+9iKNevW+cjvWwb4StOrqCovMiL0ugTQyHojKLSCj7VpC9YMKL+5hePUV5qbzse8kvduppWmCv49Nin1v5DvR7yuqtpTcwYEGGNRk/LKWTTMR2X2OwzA5pb6jpcvwTJ+i1uf1fHuwhvrpIs5JbkGiU2q0GffxG3MSsPZpBbqFIXRLZuapfnRnckf6UeAgDN20EfN9t43MgP6T+QcSMDgGD/YCZ3mexkhvcIbOLLg4Nt6Sze//Gcg9Fextfffi9h51u6zYLqa/LlwZ623FpLjy3FLM1elEh/GApBR5jNkg81m8k/GxptLbOoO6SEXW/Z+gmPg69+C/Z8nPyx9Xh2t9kE+rnXndPdPDwkCj8fWxbUQ2k6LvIy8FH7LKjntntXHgdM6zrNmgU1NT+V7Rn6ldUbGApBR2w5cYWzWQUABAX4MntQw1TuqhPntsHlI+rYt6l90jM38MQTqrmDw1cPk3hVZV33Nfm6P29R1ydUcyNtWwQwua8th+R7P551MNp1nhj4BE8MdK+sBLaG+Ads/Z1vuvf6bqSZXzNmdrOtZJckL/GeMDrEUAg6QUrJ2z+kWPsPJHS0pjLQJT/+zXbcb556KLiR++9XzR28f+R96/GE6AmEBbo5J1an+1VzMwtG2DaXNxy9zNmrN+p9zfv73M/9fdwvq9pctqxmUzbBpST338NNPNDzAXyF+ts6kHmAxCuJTmbcPhgKQSfsOptNYnouAE18THaeJroj44BaIQAIHxjypNtvkZ6uWn05de0UW9O3AqrmwWN96h80dxMF6aq5mZ7tWzC6u1JeUsK/t52p9zXT89JJz3O/rIR0gV6afZkdf3f/PdxEu2btuK/zfda+9oXhdsdQCDrhXz/Y/thnDoygjZ4D0XZoVgexM6G1+5XXQw+pVl8+OGIr4nJXx7vo3NIDXlu7HlLNAywaHWM9/urgBS7k1s9V8qFVD/HQKs/IyvDf2I6TV0FWSs1jvcyjsY8iLCuabRnbOJlz0ssS6QNDIeiAxPRcdqSo6FGTgF+M7OJliRxw5TicWGfrD/8v78nihPT8dDam2jJxLohd4EVp6sagqNYkRClzXLlZ8t529+wleIQO8RAzxtKRKteRTukc3JkxncZY+9oXh9sZQyHogH9p9g4m9+1AxxAde8BoTQE9JkKbnt6TxQkfJn9odSsc0n4IfUL7eFmiurFotO0F4fN9aWTfKPGiNE4Y8bTt+PDnkKffYj+PxdrMh9+e/5a0/DQHo28PDIXgZU5nXue7Y7bSfk+MinEw2svknIMjX9r6WhOBzrhSeIU1KWus/cfjHveiNPXjzm5h9O6gMrIWl5n58CcdxyV0GmorjGQu07XHUe+Q3gzroAojmaWZD49+6GWJvI+hELzMP7acth7f06st3dsFeVEaJ/z4GlgSwxF9J0ToN4P5B0c+oMysAvziwuIY2HaglyWqO0IIFmleFD7eeZ5rBfpNEWG3SjjwEVzXb6S11oy45swaLtzQ74qmITAUghc5cTmfdUm2eslPjtbx6iD7DCRqqqCO/K1Hb/f006rVhcsFl+2S2P087ucIT6bU6PG0ah5kXJ921rrLN0rKWVzHuISnhzzN00M8KysxY6B9vDouL9a1x9GAtgPo36Y/oJLevXv4XSczbm1cUghCiHFCiJNCiBQhxO+q+dxfCLHc8vkeIUSU5XyUEKJICJFoaf/WzBkghDhimfNP4dG/WH3y902nrMdjeralb2RLL0rjhG3/q1kdjIToER693aRJqtWF95Les60OQuMYEe5ZWYmYpJoH8TEJnhpjS9W95KdUsuqwlzCp+//f3nmHR1Wlf/zzzqRXAoQWCKEjvRmKhSYqiqKiiMqKXVF0UVcFRBd1cde1sSqoqNhWBX6sKDZsCBaQHkqkGIoQICQQSELaZGbO748zmZmEZBIgyb3g/TzPeWbOnXtvvpNk5j3nPed938u4rEPtakUEBj/q66+ZY9q1BBFhQk/ftulFOxb9qdcSqjQIImIHZgLDgU7AdSLSqdxptwJHlFJtgReBZ/xe26GU6uFpd/kdfxW4A2jnaRef/Ns4/di8L4evU31rB/cPq4G8/LVF1nbYNN/XHzy11n/ktm26nSj7ju3j4zRfgrV7et5Tu7MDgNxtutUyl3RpSkePS7GwxMXrJxGXsO3QNrYdqoMtlu2GQfOz9XOXQ7sbTcrZTc6mb5O+ALiUi9c2vFbFFWcu1ZkhJANpSqmdSikHMBcoX4R2JFCaLGYBMDTQiF9EmgIxSqkVSikFvAdcccLqT2P8ZwfDuzShc7NYA9VUwdJ/6lKJoN0BiX1r/UfeeaduJ8rsjbNxunVRmV6NetG/af8aVlYBq+7UrZax2YT7h7X39t9b8QeZnprb1eXOz+/kzs9rX6ueJUzx9de9D0dqvgJcTeE/S/hi1xfszDHx9t5apDoGIQHwD21M9xyr8ByllBPIARp4XmslIutFZJmInOd3fnoV9wRARO4QkTUisiYr68yocpSy9yjfb80E9Odm4gXtq7jCQA6m6iCjUvw/5CZjT+6eMjuLJvScUPuzgzrmwk6N6ZKgdxwVO93MWnrq0cu1RuvBkDhAP3eXwI//NlZPAHo06sE5Cb4dR6+mvFrFFWcm1TEIFX2iyue3reycA0CiUqon8ADwoYjEVPOe+qBSs5VSfZRSfeLjazgHjQEopfjXV1u8/RHdmpl7Z9F3T+D907QfDgnm3Vn08vqXveUx+zbpy9lNzjZYUc0jIjzgN0v4YOUf7DlcYKCiAIjAEL+1hJQPIXOrcXqq4J7uvmI/i3cvJvVwqoFqjKE6BiEd8E+72RzYX9k5IhIExALZSqlipdRhAKXUWmAH0N5zfvMq7nlGsmRrJr/u1LVnyy8Umo5dP8LvX3s65T7cJmNj1sYyUcn+LoAzjcEdGnmr6JW4FP/+2rxfsiSdq2cKoN2O3/3dWD0B6BrflSEthnj7z695HmXS2g61RXUMwmqgnYi0EpEQYAywqNw5i4DS+nRXA0uUUkpE4j2L0ohIa/Ti8U6l1AEgT0T6edYabgQ+5QzH6XLz9Je+2cENfRNpEx9loKIAuN3wjd/icY/roUlX4/QEQCnF82ue9/aHtRxGj0Y9DFRUu4gIUy7xRYh/vvGAueslXPgUXqfA9sWmrpcwsfdE7Pori9UZq/909RKqNAieNYEJwNfAFmC+UipVRJ4UkdL0hm8BDUQkDe0aKt2aej6wUUQ2oBeb71JKZXteGw+8CaShZw5f1dB7Mi3z1uxlR5audxAVGsRfh5p4drDp/+DABv08KLzsNsI6YOpU3arDkr1LWJe5DtD1Dib2mliLyiqgy1Td6pDeLeO4pKuvmt7TX26p1mh26vlTmXp+3WqlSVfo7leD4pupesBhQlrFtipTL+GFtS94Nyn8GZDTaUrUp08ftWbNGqNlnBTHip0Menapd+/4Qxd14B6zBqKVFMErfaA0TfJ5D8LQx43VVAkl7hKu+vQqdufuBmDsWWN5JPkRY0XVEbsP5TPsxWWUuPRn+PW/9DZvydWcffByLx2oBnDVG9BttLGaKuFw4WEuXXgp+SV68PZYv8cY3cGcWquLiKxVSlUZrm9FKtcRry/b4TUGTWPDuOUcE9c7+HWWzxhENIRz6njEDaSk6FYV87fN9xqD6OBo7uxWB1sqy3MkRbc6JqlhJGP7tfT2//XVVoqdroDXpGSkkJJhQEGY2ATod7ev//2T4DDnYniD8AZl6mbMTJlJniPPQEV1h2UQ6oDdh/J5fZlvX/ODF3YgPMRuoKIA5KTDj8/6+oMmQVhMncuYOFG3QBwqPMTM9TO9/du63Ua9MAOivddO1M0A7hvSjugwXf1r16F83vo5cOK7iYsnMnGxMVo59349wAA94PCvq2EyxnYaS+OIxgBkF2UzK2WWwYrqBssg1DJKKaZ9lorDpX2m3VvU46qeFYZcmIOvp0CJZ+TWqDP0vtlYPQGYsXYGeSV65JYYncjYs8YarKjuiYsMKbMN9eXv09h/ikV0ao2wGLjAb5fRL//RObJMSHhQOA/28eV8+mjrR2w/sj3AFWcGlkGoZb797SBLt+mAOhH4x8gu2GwmDZbasQR+89vsdelzYDdnXef1mev5dIdP6+S+kwmxhxioyDj+0q9lmZQW//jiN4MVBaDHWEjwuLJdDvjqEV0f1IRcnHQxyU2SAZ3SYvqv08/4baiWQahFCh0unvjM9+G8PjmRrs1NmqLC6YAvH/b1u43Rue1NiNPtZPqv0739oYlDOTfhXAMVGUuQ3caTI33Ff77clMGP200a1W+z6YFG6TbUtG9h6xeGSqoMEWFK3ykEiR4Urctcxxe7zKm1prAMQi3yyg+/e2vgxkUE89BFHQxWFIAVL8NhT22G0BgY9qSxegIwd+tcth3RCdrC7GE8fPbDVVxx5pPcqn4ZV+TfF6VSVBJ4gdkwmvWEPrf4+osnQ/Ex4/QEoE29Nozt5HNFPr/meXIduQYqql0sg1BLbN6Xw2t+C8mPXNyRehEmdWlkbYOlfglqB0+B6MbG6QGeflq38uzN28tL61/y9u/odgfNoprVobIK6P60bgYz6ZKORIf6FphnfPf7cec8PfRpnh5qvFaGTIVwXSuanD1615FJuav7XTQKbwTojQzPrTZv5tZTxTIItUCJy83DCzbicmt/49lJcYzu06KKqwzC7YJPJ4DLk1u/WU842/hykwMG6OaPUoppy6dR6NSzrrb12jKu87gKrq5j4gfoZjCNosN4ZHhHb3/2jzvYsPdomXMGtBjAgBbGayWiPlz8L19/1evwx3Lj9AQgMjiSKX19SR0Xpi3kl32/GKio9rAMQi3w2tId/HZATytDg2z8++ru5l1IXvkapK/Sz23BMHKmKRaSly/XzZ8Fvy9gVYbWahMbTw540hwLyVnLdTMB1ycn0q+1Hnm7FTy8YCMOpy8qePne5Szfaw6tdBsN7S7y9T+dYNrYhKEth3JRkk/rtBXTOOYwp5vrVLAMQg2z/WAeLy3xTdX/dmEHWjWMNFBRAA7vgO+f8vXPfwgadzZOjx9TpuhWSkZ+Rpl8ReM6jaNrvElyK22YopsJsNmEZ0Z1IzxYx7lsO5jHzB/SvK9P+X4KU743h1ZEYMSLes0KIHsHLDWBO6sSpvSdQlyoTiqYkZ/BjHUzDFZU81gGoQYpdrq4f16KN5VA9xb1uOVck0Yku5zwyXjwuF9o3EUHDpkQt3Iz9Zep3lQCSTFJ3N3j7iqu+vPSskFkmQ0MM39II6Wc68g0xCbAhf/w9VfMhN3mdMfUD6vP5L6Tvf152+bx876fDVRU81gGoQZ5dvE2UvdrV1GI3cazV3fDblZX0bJnYO9K/VzsMPIVCDKB+6UC3t78NisPaK2C8MSAJwgLCjNYlbkZNyCJPp4U2U634q9z13Os2KRJ2nrdCK0H6efKDR/fDgXZga4wjIuTLmZwi8He/qM/P8qhwkMGKqpZLINQQyzdlsmbfmkDJg3vSPvGJi18s/vnsjVuB0/Ri8kmZFPWJl5Z/4q3f1vX2+jVuJeBik4P7DbhhdE9iPLsOvrjcAGPf7LZYFWVIAJXvArh2oCRuw8W3WvKgDURYdqAaTQM1yk4souymfrzVNzKnNlbTxTLINQAmXlF/O3/Nnj7Qzo24uZzkowTFIiCbPj4Dl+N5KTzTOsqcikXD//4ME6lR7bdGnZjfI/xBqs6fUhsEMH0K30Bax+v3+dNsGg6YprpDQ2lbP0c1r5tnJ4A1A+rz/RzfYGRv+z/hfd/e99ARTWHZRBOEafLzf3zUjh0zAFAfHQoz17dzZy1fN1u+ORuPQIDvQ/8qtlgM1+ivRdfVLT+y0ukH9Olt6OCo3jm/GcItgUbrKwCes/QzYSM7JHAqF6+4oSFmWN5INmkC7cdLy275XnxZDiw0Tg9ARjQbAA3d/Hl+ZqxbgYbsjYEuOL0oFoGQUQuFpFtIpImIpMqeD1UROZ5Xl8pIkme48NEZK2IbPI8DvG7Zqnnnime1qim3lRd8szirfySdhjQM98XR/egQVSowaoqYdkzsN2vDtEVs/TIzISkBL/DuuA53v5j/R6jeXTzyi8wkrgeupmUJ0Z2JqlBBAAuRxIzvnSQW1RisKpKuPApaNRJP3cWwdwbIP+wsZoq4d4e99K5gd6V53Q7uf+H+8kqMGnKkGpSpUHwlMCcCQwHOgHXiUincqfdChxRSrUFXgRKw14PAZcppbqiS2yWn1fdoJTq4WmZp/A+DOHTlH288ZNv3eDeIe04t11DAxUFYMvnsMwvEKj/BOgw3Dg9Afhl3y889f4KjqX2A2B0+9Fc0voSg1UFIOM73UxKVGgQs27oTViwjUJbCqnZvzBxbgput/l89ASHwzXvQohn/S1nDyy4Se+KMxnB9mCeG/gcsaE6P1lWYRb3L70fh8thsLKTpzozhGQgTSm1UynlAOYCI8udMxJ41/N8ATBUREQptV4ptd9zPBUIExGTDp9PjM37cnh4gW86e8FZjZlo1pKYmVthoV/hmNaD4IInjFITkL25e3nox4c4+OntZC66g56NejIp+bhJqbnY/A/dTEynZjH8++ru5ATNJSdoLku2ZvLidyZN5xzfXrsyS9n1I3xrzop9zaOb8+z5z2IT/VW6IWsD/1z1T4NVnTzVMQgJwF6/frrnWIXneGow5wANyp0zClivlPJf1Xrb4y56TEzpdK+Y/UcLuf29NRR7IkDbxEfy4rUmjUbOOwgfjobSqMp6LeHqt00RjVyeo0VHuWfJPd7qVCH2YF4Y9ALBdhOuG5yGXN69Gc3qhXv7Ly9J4+N16QYqCkDHS2CQXwDdrzNhzZzKzzeQ/s3680DvB7z9BdsX8G7quwGuMC/VMQgVfcuVn2sGPEdEOqPdSP71DW/wuJLO87S/VPjDRe4QkTUisiYry3j/XE5BCePmrOJAjq4NGx0axOwb+xAdZsIvreI8+OBqOPqH7gdHwJgPdR4Zk1HoLGTCkgnsytEuOJsIbeu19W7vs6gZWtSPIDbc97/68IKNLDNrquzzH4KOI3z9Lx7Urk8TcmOnG7m09aXe/nNrnuOLnadfquzqGIR0wD8zW3Ngf2XniEgQEAtke/rNgYXAjUopb3kkpdQ+z2Me8CHaNXUcSqnZSqk+Sqk+8fHx1XlPtUZRiYvb3lvN75l6tB1sF177S2/axEcZqqtCnA6YNxYyPG4tseuZQZMuga8zAKfbycPLHvbu0hCEVrGtiQw24e/1NEeAdo2jvQV1nG7F+P+uZWO6CSOZbTa48nVfjIxyw/9uhT9WGKurAkR0wGSvRr4Ymam/TGXFfvNpDUR1DMJqoJ2ItBKREGAMsKjcOYvQi8YAVwNLlFJKROoBXwCTlVLeeHQRCRKRhp7nwcAIwKRRMxqH082ED9ezevcR77HnrunOOW1NOIJ1OeGTu2DnUt+xy2ZAh4sNk1QZbuVm2vJpLE1f6j32SPIj1A8z3yzmTCHIJrxzczIJHvdRgcPFzW+v5veDJiwkHxoF1/8f1G+t+84i+OhaU25HDbWH8tKQl2hbry2gBzoTf5jIxizzaa0MqU5JOBG5BJgB2IE5SqnpIvIksEYptUhEwtA7iHqiZwZjlFI7RWQqMBnwT8x+IZAP/AgEe+75HfCAUipgRY8+ffqoNWvWnOh7PGUcTjd3f7CO77Yc9B6beulZ3HZe6zrXUiUuJyy8Azb/z3ds8FQY+JBxmirB5Xbx9+V/L1MK85Yut3B/7/vZpuvf0MHENYW85HrExphf7LZDWmuHhh1Iy8xj1KsryCnUW1AbRoXw0e39aGfGCPvsXfDWMMj3uLfC4+DGT6Fpd2N1VUBGfgZjvxzLwQL9fREVHMVrw16je7xxWkVkrVKqT5XnnU41Qo0wCMVOF/d8sI7vtvh2xd45sDWTh59VpzqqhatE54FJXeg7lnwHDP+3DpIwES63i8eXP86iHb7J5hVtr+DJAU+aM6jvDGXtH0e48a2V5Dv0WKxBZAgf3t6PDk1MaBQObIB3L4OiHN0Pq6eNQjPzxYCkHUnjlq9v4Uix9ihEBkfy2gWv0aORMVqraxCsSOUAFDic3Pn+2uOMwaSLOwa4yiBKimDBzaeFMShxlTDl5ylljMGVba/kiQFPeI3BZ5/pdlqQ/plupwGfbfuMz7b5tPZuGce7tyQTGaKj1Q/nO7j+jV/ZlJ5jlMTKadpdG4AwT13yoqPw3uWwZ6WxuiqgbVxb3rroLa/rM78knzu/vZNVB1YZrCww1gyhEjLzirj1nTVs2uf7YNw9qA0PXdTBfCPYgmz46DrY+6vvWN+7dEUqk2nNdeTywA8PsDLD9yEe1W4Uj/d/3LuXG2DQIP24dGnd6jspvhukHy9YaqSKajHonUEALL1paZnja//IZtyc1d6MqBEhdmZe34vBHU2YQGB/Crw3UhsEgKAwHbfQqXx4lPGkHUnj1m9uJbtIZ28NsgXx1DlPMaL1iCqurFmsGcIpkJZ5jKtmLS9jDO4b2s6cxqDUt+pvDPpPMKUxyMjPYNxX48oYg9HtRx9nDCzqnt4t6/PercneLakFDhe3vruaD1fuMVhZBTTrAeMWQYRnQ4ezCOaPgxWzjNVVAW3j2jLnojnemsxOt5PJP03mjY1vYMbBuPUpLMe3vx3kylm/kH5EF46xCUy/sgsPDGtvPmOQ9j28MQQOl1bEErjoabhouumMweqM1Yz5fAxpR33Vu+7reR9T+021jIFJ6JUYx//G9/fuPnIrmLJwE49/upliZ8D9HnVP0+5w27dQv43ngIKvJ+synCWFhkorT5t6bfjvJf/17j4CeGn9S0z6aRIFJeYqGWp9Ej04XW6eWbyV299bQ16RnjaHB9t5c1wfbujb0mB15XC7Yekz8N9RUOgpJGIPhWvegf73GCqtPEop5myew+3f3M7hIp2kLMgWxNPnPs3t3W43n5H9k9O2UTQL7xlAl4QY77H3VvzB6Nd/Zd9Rc33RUr813PotNPcLYVr/Prx1oZ45m4imUU15d/i7JDfxaf1y15fc8OUN3mBMM2AZBGBvdgE3vLmSV5d64+ZIqBfO/Dv7M6RjYwOVVUDOPvhglKf2rGfKGdUExn0Gna8wVFp5DhUe4r4l9/Hi2hdxeXYU1w+rz+xhs7mszWUGq7OojEbRYcy7oz/DuzTxHtuw9ygjXvqJxZszDFRWAZENtPuo62jfsYyNMHsgbFpgqiI7xooH+QAAEWlJREFUMSExvHrBq4xqN8p7LO1oGmM+H8OnaZ+awoX0p15UVkrx0aq9TP/iN++2O4CB7eOZcW0P4iJNVFJSKdgwF756BIr9doAknQdXz4Eocy3+Ld61mOkrp3O02BcB2yO+B88NfI7GkVUb2b2e7FktWgQ+zxTke8RGml/s3hyttUVs1VqVUrz18y7++dVWXH6ZUa/o0Yxpl3emXoTJPh9r3tI1FPyzjXYaCZe+AJHmCiBd+PtCpq+cTrHLl9ptYPOB/L3/34mPqPmMDFYcQhXsyDrGtEWp/PS7rx6qTfTi8X1D2pkrUV32Llg8CbYv9jsocO5EHXRmokR1B44d4Nk1z/LtH9+WOT72rLE80OcBcxa4sQjI6t3Z3PvhejJyi7zHGkWH8tiITozo1tRcbr99a2H+TTptdikRDfW6WtfROh2GSdiavZUHlz7Injyf1piQGB7o/QBXtL0Cew0WrrIMQiXkFZXw8pI05vy8C6ffqKd1fCTPXdOdXolxpyqz5nDkw08vwPKXwW8kQVwSjJwFSecYJq08Rc4i3k59mzmb5lDk8n1xNI1syhMDnqB/s/4ndL958/TjtdfWpMpa4g+P2JbmFztvs9Z6bZcT05pTUMITn6fy8bp9ZY4nt6rPtMs606lZTCVXGkBRLnwzFdaVyzjaPBmGPwMJ5qnJXVBSwIx1M/ho60dljndq0InJyZNrLJDNMgjlKHS4+GDlH7y2bIe33CXozTi3ntOKv13UgbBgk5SSLCmCde/BT8/DsXI+27Nvh2FPQEikMdrKUeIq4ZMdnzB742wy8stqHdVuFH/r8zeiQk48SZ0Vh1A7VBaHUF2+Sc1gysLNZWoz2wSu6JnAfUPakdTQHP+XAKR9B5/eC3n+uTgFuoyCgY/ougsmYdWBVTy+/HH2HStrcIe1HMb47uNpF3dqtVYsg+ChqMTFhyv38OqyHWTllS0w3qdlHNMu70yXhNialHnyOPIh5UM9K8grl1A2oTcMfxaa9zZGWzmKnEV8tvMz3tz4Jvvzy2o9q/5ZTEqeRK/GJz8SswxC7XCqBgEgt6iEl777nXeW7y4zy7bbhFG9ErhzYBvzZAAuztMDqxUzy64tiA26XA3n3g+NyxeANIZCZyFzNs9hzqY5ONx+g1aEC5MuZHz38bSp1ybAHSrHMggeRr+2glW7s8scaxobxqThHbm8ezNz+D+P7oFVs/WsoKhcyoCoJjD0ceh+nSn8nxn5GczbNo8F2xeUWTAGvYNoQs8JXNX2qlP2f1oGoXaoCYNQSlpmHk99vqXCegoD28dz0zlJDGwXb471uMM74OtHy9YUL6XVQOg3HtpdCDXotz9Z0vPSeWHtC8etwwnC+5e8f1JJ8qprEMyzGllLXNOnudcgNI4JZcLgtow+uwWhQQb/4YuPwZbPYMNHukRg+ZpDkY306KXPzbrOrIEUOgv5Yc8PLNqxiBUHVuBW7jKvx4XGcXOXm7m2w7VEBEcYpNKirmnbKJp3b0lm9e5sXvx2O8t3HPa+tmx7Fsu2Z5FQL5wreyZwVa8EWhs5a2jQBq6fC+lrYOk/tTuplF3LdItuBt1GQ4/rId64zLXNo5vzwqAX+O3wb7ya8qo3NXy7uHZ0bdi1Vn/2GT9DcLrcXP/mSi7p0oQxyYnGrhMUHoHtX8PWz3WUcUVRinGtdB6iXjdCiHFfrnmOPH5K/4nv93zPz/t+psB5vNaEqASu63gd17S/psYNgTVDqB1qcoZQnlW7snnjp518t+Vghdv/OzeL4cJOTbioS2M6NI42dna+d5XerLH1c114pzyNu0DHS3XFtiZdDY38Tz2UyqwNs7iy7ZVc0PKCk7qH5TIyA458vQ1u5zJdrGb/uor/+RBoM1hnJzVo2lroLGTzoc2syljFr/t/ZdOhTd5gsvL0bdKX6zpex6AWg2p0a5w/hzy7gRuaa/t4xRR5xIaZX+yhAq21YUTtad1zuIB3V+zmf+vSOVpQUuE5TWPDGNCmIee2a0ByqwY0iw0zxkAc3QOr3tBrdwWHKj4nqgm0HgStB0LLAbouuRlczSeAZRDqGkcBZG6Bg5t03vb0NXAwFQLV/GnYAbqPgW7XQmxCnUktdhWTdiSNbUe2seXwFjYe2sj27O04lbPSa5JikriszWWMaD2CZlHN6kyrxemLw+lmydZM/rcunaXbMilxVf5d0zgmlJ4t4ujaPJZOzWLo3DSG+OjQujMSrhLtRkr5UM/iXcWVnxvZCFok6yR7TbrpGUR0U1MbiRo1CCJyMfAfdHWzN5VS/yr3eijwHtAbOAxcq5Ta7XltMnAr4ALuU0p9XZ17VoShBkEp7fLJ3a9HFUf3wJHdcPh3OPS77pdfBzgO0XugO47QrZa2vSmlyHXkcrDgIAeOHSD9WDr7ju1jd85udufuZt+xfcetA1REpwadGNJiCEMTh9KmXps6HcG9845+vOmmOvuRJ8/Od/Rj65uMVFEt3kl5B4CbetxUpz83r6iEH7Zl8U1qBsu2ZZFXXPngo5TY8GBax0fSJj6KpAYRNI+LoHlcOM3qhRMfHUqwvZY2WRTnaZfu1s/h92+O3+hREaGx0LCdbvVb61lEvUSIbQ7RTcBubEBmjRkEEbED24FhQDq6xvJ1Sqnf/M65G+imlLpLRMYAVyqlrhWRTsBHQDLQDF0qs/RbMOA9K+KUDYLLCc5CnQ3Rke9rxXlQnKv/8EVHofCoThqXf1iX7MvPhLwMnWb3hBBodBYk9tNTzqTzIKJ6tYJdbhfFrmIKnYUUOAv0Y0kB+SX5HCs5Rp4jj1xHLrnFuRwtPsqRoiNkF2VzuOgwWQVZZYLDqkvr2Nb0bNSTfs36kdwk2dC6xtYaQu1Qm2sI1cXpcrNpXw6/pB1ixc7DpOw5WiZ1THUQgQaRoTSKDqVBVAgNo0KJiwghNjyY2PAgYiOCiQoNJio0iOiwIMJD7ESE2IkIDiIsxEaI3Va9AY7bBQdStNt314/aBVyce4LvWHTqjKgm+jEyHiIaQHg9XQo0LBZCYyA0WteQDomC4Ai9hhgUDkGhpzz7qMldRslAmlJqp+fGc4GRgP+X90hgmuf5AuAV0b/tkcBcpVQxsEtE0jz3oxr3rBGWf/swS7Yv1K4bz6jY3wSWf67w/OLF95qyg6oXgSLCdwxBec5xey5whUahwmJxh0bjCotBhcXgEhtuVYBr72e49nyCS7lwuV2UuEtwKiclrhKcbicOt4MSVwkOt4NiVzFOd9UjqJNFEBJjEukQ14EO9TvQqUEnujbsSmyoSeIxLM5oguw2eibG0TMxjglD2uFyK7YfzCNl71F+25/LlgO6BTISSsGhY8VlAuROBBEIC7ITEmTTza4fg2xCsN1GsF2w24Qguw27CHbbOdhs5xLU2EVz117aFG8l0bGDFo4dJDh2Eu7OD/DTlGdgefz23OrgRnBKCAUh9ak3eetJ3aO6VMcgJAB7/frpQN/KzlFKOUUkB2jgOf5ruWtLneVV3bNG2FZ0iHlRYbVx6wpwg+sIFBwBg9OchweF0ziiMU0jm5IQnUBCVAKJ0YkkxSaRGJ1IWFBd/U4sLAJjtwlnNY3hrKa+9BdKKQ7mFrMj6xg7s46x90gh6UcK2JtdyIGcIg7nF59SIlOloLDERWHJydR5iER7x0uDRBWNOEob235aywFaSBbNJZMWkkVTyaYhOdjk5MXaUISoYnKLaz/9eHUMQkVzlfLvrrJzKjtekfOvwt+YiNwB3AGQmJhYucrKMNh3d7IIQlhQGKH2UCKCIggPCic8KJyokCiiQ6KJDI4kJiSG2NBYYkJiqB9W39viI+KJCo4yR9CdhcVJICI0iQ2jSWwY57Q9fkdUictNZl4xh/KKyc53cOhYMUcLSjha6CCnsIScQif5xU6OFTnJK3ZS6HCS73BR5HBR5HQFXOA+CbVkEkemO44VdD7uVTsu4jlKQ8mhoeTSUHKoxzFiJZ9Y8omVfKIoJEoKiaaQcIqIkGLCKSYMByGijVYxtZ9dtjoGIR3wz5XbHNhfyTnpIhIExALZVVxb1T0BUErNBmaDXkOoht4y9Os9nkcz+2nDIHavL078bFX5L07xO6f0PJHjn5d/tIsdm2jfpE1s3r7/Y5AtCLvNTpAEEWQLItgWrJtdP4baQwmxhxBsC7a+0C0sKiHYbiOhXri3utuJ4nIrip0uHE43xU43DqebEpebEpeixOXG6Va43LrvditPX+FWvkelwOXpg551uNxKu56Vfiwd5ir0+V6Xs9LHAPIU5JUe9xfpmQKJcmF3FRNud1PbexGrs6gchF4AHgrsQy8AX6+USvU75x6gq9+i8lVKqdEi0hn4EN+i8vdAO/TMIeA9K8LU204tapQCj8st4nQIfC4N2gsyv9jSko1WRPmfixpbVPasCUwAvkZvEZ2jlEoVkSeBNUqpRcBbwPueReNsYIzn2lQRmY9eLHYC9yilN+ZXdM+TeaMWZyanhSEo5TQwBKVYhsAiEFZgmoUpmTVLP959t7E6qsV2j9j25hc7a7XWevfZ5tdqUXNUd4ZgfPpMC4sKmD9ft9OCPfN1Ow2Ynzqf+amnh1aLuscyCBYWFhYWgGUQLCwsLCw8WAbBwsLCwgKwDIKFhYWFhYfTapeRiGQBfxitowIaApUkUzcdltbawdJaO1haa4aWSqn4qk46rQyCWRGRNdXZ0mUGLK21g6W1drC01i2Wy8jCwsLCArAMgoWFhYWFB8sg1AyzjRZwAlhaawdLa+1gaa1DrDUECwsLCwvAmiFYWFhYWHiwDEINIiL3isg2EUkVkX8bracqRORvIqJE5PgKJCZBRJ4Vka0islFEFopIPaM1lUdELvb83dNEZJLReipDRFqIyA8issXzP/pXozVVhYjYRWS9iHxutJZAiEg9EVng+V/dIiL9jdZ0MlgGoYYQkcHoutDdlFKdgecMlhQQEWkBDAP2GK2lCr4FuiiluqFraEw2WE8ZRMQOzASGA52A60Skk7GqKsUJPKiUOgvoB9xjYq2l/BXYYrSIavAfYLFSqiPQndND83FYBqHmGA/8SylVDKCUyjRYT1W8CDxMJaVLzYJS6hullNPT/RVdXc9MJANpSqmdSikHMBc9MDAdSqkDSql1nud56C+t2i7CddKISHPgUuBNo7UEQkRigPPRdWFQSjmUUkeNVXVyWAah5mgPnCciK0VkmYicbbSgyhCRy4F9SqkNRms5QW4BvjJaRDkSgL1+/XRM/CVbiogkAT2BlcYqCcgM9KDFbbSQKmgNZAFve9xbb4pIpNGiTobq1FS28CAi3wFNKnjpUfTvMg49FT8bmC8irZVB27iq0DoFuLBuFVVOIK1KqU895zyKdnl8UJfaqkFFha9NPesSkSjgf8BEpVSu0XoqQkRGAJlKqbUiMshoPVUQBPQC7lVKrRSR/wCTgMeMlXXiWAbhBFBKXVDZayIyHvjYYwBWiYgbndskq670+VOZVhHpCrQCNogIaBfMOhFJVkpl1KFEL4F+rwAiMg4YAQw1ysAGIB1o4ddvDuw3SEuViEgw2hh8oJT62Gg9ATgHuFxELgHCgBgR+a9SaqzBuioiHUhXSpXOthagDcJph+Uyqjk+AYYAiEh7IAQTJrpSSm1SSjVSSiUppZLQ/8y9jDIGVSEiFwOPAJcrpQqM1lMBq4F2ItJKRELQ9cQXGaypQkSPAN4CtiilXjBaTyCUUpOVUs09/6NjgCUmNQZ4Pjt7RaSD59BQdB350w5rhlBzzAHmiMhmwAGMM+Fo9nTkFSAU+NYzo/lVKXWXsZJ8KKWcIjIB+BqwA3OUUqkGy6qMc4C/AJtEJMVzbIpS6ksDNZ0p3At84BkU7ARuNljPSWFFKltYWFhYAJbLyMLCwsLCg2UQLCwsLCwAyyBYWFhYWHiwDIKFhYWFBWAZBAsLCwsLD5ZBsLCwsLAALINgYWFhYeHBMggWFhYWFgD8P85nHzYHdL0oAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "\n",
    "mu = 0\n",
    "variance = 2\n",
    "sigma = math.sqrt(variance)\n",
    "x = np.linspace(mu - 5*sigma, mu + 5*sigma, 100)\n",
    "y1 = stats.norm.pdf(x, mu-2, variance)\n",
    "y2 = stats.norm.pdf(x, mu, variance)\n",
    "y3 = stats.norm.pdf(x, mu+2, variance)\n",
    "plt.plot(x, y1, x, y2, x, y3, lw=3)\n",
    "plt.axvline(x=mu-2, c='b', linestyle='--')\n",
    "plt.axvline(x=mu, c='orange', linestyle='--')\n",
    "plt.axvline(x=mu+2, c='g', linestyle='--')\n",
    "plt.legend(['mean: -2', 'mean: 0', 'mean: 2'])\n",
    "x1 = np.linspace(mu - 5*sigma, 0, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "import math\n",
    "\n",
    "mu = 0\n",
    "variance = 2\n",
    "sigma = math.sqrt(variance)\n",
    "x = np.linspace(mu - 5*sigma, mu + 5*sigma, 100)\n",
    "y1 = stats.norm.pdf(x, mu, variance-1)\n",
    "y2 = stats.norm.pdf(x, mu, variance)\n",
    "y3 = stats.norm.pdf(x, mu, variance+1)\n",
    "plt.plot(x, y1, x, y2, x, y3, lw=3)\n",
    "[plt.axvline(x=x_, c='blue', linestyle='--') for x_ in [mu-1, mu+1]]\n",
    "[plt.axvline(x=x_, c='orange', linestyle='--') for x_ in [mu-2, mu+2]]\n",
    "[plt.axvline(x=x_, c='green', linestyle='--') for x_ in [mu-3, mu+3]]\n",
    "plt.legend(['var: 1', 'var: 2', 'var: 3'])\n",
    "x1 = np.linspace(mu - 5*sigma, 0, 50)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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3uypMkjR1DBoWL+60CknSlNZ2b6i9gTcDTwa+D1xQVZu2R2GSpKmj7WqoC4EhekHxYuCjnVckSZpy2qahDq2qpwMkuQD4bvclSZKmmrYji99uXnD6SZJ2XW1HFn+Q5JfNcoBHNOubr4ZqvU25JGnHN2ZYVNW07VWIJGnqGvTeUJKkXZhhIUlqZVhIkloZFpKkVoaFJKmVYSFJamVYSJJaGRaSpFaGhSSplWEhSWplWEiSWhkWkqRWhoUkqZVhIUlqZVhIklp1GhZJ5iVZl2R9koWjbD82yQ1JNiU5ZcS205L8uHmd1mWdkqSxdRYWSaYBi4EXA4cCpyY5dES3nwKvBz4/YuyjgXOAY4CjgXOSHNBVrZKksXV5ZHE0sL6qNlTVfcAy4OT+DlV1S1V9D3hgxNgXAVdV1Z1VdRdwFTCvw1olSWPoMiwOBG7tWx9u2iZsbJIFSVYlWXX77bdvdaGSpLF1GRYZpa0mcmxVLamqoaoamj59+riKkyQNrsuwGAZm9q3PADZuh7GSpAnWZVisBOYmmZNkT2A+sHzAsVcCL0xyQHNi+4VNmyRpEnQWFlW1CTiD3l/yPwQuraq1SRYlOQkgyTOTDAOvBj6dZG0z9k7g/fQCZyWwqGmTJE2C3bvceVWtAFaMaDu7b3klvSmm0cYuBZZ2WZ8kaTD+gluS1MqwkCS1MiwkSa0MC0lSq05PcO9IZi/88mSXMJBbzj1xskvQBJmM/+eWbbgDgPnj+Gz/nxN4ZCFJGoBhIUlqZVhIkloZFpKkVoaFJKmVYSFJamVYSJJaGRaSpFaGhSSplWEhSWplWEiSWhkWkqRWhoUkqZVhIUlqZVhIkloZFpKkVoaFJKlVp2GRZF6SdUnWJ1k4yva9klzSbP9OktlN++wkv06ypnl9qss6JUlj6+yxqkmmAYuBE4BhYGWS5VV1U1+3NwF3VdWTk8wHPgi8ptl2c1Ud0VV9kqTBdXlkcTSwvqo2VNV9wDLg5BF9TgYubJYvA16QJB3WJEnaCl2GxYHArX3rw03bqH2qahPw78Bjmm1zktyY5JokzxntA5IsSLIqyarbb799YquXJP1Ol2Ex2hFCDdjnZ8CsqjoSOAv4fJL9HtaxaklVDVXV0PTp07e5YEnS6LoMi2FgZt/6DGDjlvok2R3YH7izqn5TVXcAVNVq4GbgKR3WKkkaQ5dhsRKYm2ROkj2B+cDyEX2WA6c1y6cA36yqSjK9OUFOkoOBucCGDmuVJI2hs6uhqmpTkjOAK4FpwNKqWptkEbCqqpYDFwAXJVkP3EkvUACOBRYl2QTcD7y5qu7sqlZJ0tg6CwuAqloBrBjRdnbf8n8Arx5l3OXA5V3WJkkanL/gliS1MiwkSa0MC0lSK8NCktTKsJAktTIsJEmtDAtJUivDQpLUyrCQJLUyLCRJrQwLSVIrw0KS1MqwkCS1MiwkSa0MC0lSK8NCktTKsJAktTIsJEmtDAtJUivDQpLUyrCQJLUyLCRJrToNiyTzkqxLsj7JwlG275Xkkmb7d5LM7tv27qZ9XZIXdVmnJGlsnYVFkmnAYuDFwKHAqUkOHdHtTcBdVfVk4G+ADzZjDwXmA4cB84BPNvuTJE2CLo8sjgbWV9WGqroPWAacPKLPycCFzfJlwAuSpGlfVlW/qap/BdY3+5MkTYLdO9z3gcCtfevDwDFb6lNVm5L8O/CYpv36EWMPHPkBSRYAC5rVe5Ksm5jSJ8xjgV9M5A7zwYnc27jtbN8Hdr7vNOb3edbmhQ++dOAd+t9owk2173PQIJ26DIuM0lYD9hlkLFW1BFgy/tK2jySrqmposuuYKDvb94Gd7zvtbN8Hdr7vtKN+ny6noYaBmX3rM4CNW+qTZHdgf+DOAcdKkraTLsNiJTA3yZwke9I7Yb18RJ/lwGnN8inAN6uqmvb5zdVSc4C5wHc7rFWSNIbOpqGacxBnAFcC04ClVbU2ySJgVVUtBy4ALkqynt4Rxfxm7NoklwI3AZuA06vq/q5q7dCUnSLbSjvb94Gd7zvtbN8Hdr7vtEN+n/T+IS9J0pb5C25JUivDQpLUyrDoQJKlSW5L8oPJrmUiJJmZ5FtJfphkbZIzJ7umbZFk7yTfTfIvzff5i8muaSIkmZbkxiRfmuxaJkKSW5J8P8maJKsmu56JkORRSS5L8qPmz9Oz2kdNDZ6z6ECSY4F7gH+sqsMnu55tleSJwBOr6oYkjwRWAy+vqpsmubSt0twlYJ+quifJHsB1wJlVdX3L0CktyVnAELBfVQ3+q7spKsktwFBVTegP2CZTkguBa6vq/OYq0d+rqn+b7LoG4ZFFB6rq/9C7umunUFU/q6obmuW7gR8yyi/qdxTVc0+zukfz2qH/1ZRkBnAicP5k16LRJdkPOJbeVaBU1X07SlCAYaFxau4MfCTwncmtZNs0UzZrgNuAq6pqh/4+wHnAu4AHJruQCVTA15Ksbm7ts6M7GLgd+J/NdOH5SfaZ7KIGZVhoYEn2BS4H3l5Vv5zserZFVd1fVUfQuzvA0Ul22OnCJC8Fbquq1ZNdywR7dlU9g96dq09vpnd3ZLsDzwD+vqqOBO4FHvbohqnKsNBAmrn9y4HPVdUXJrueidJMA1xN71b4O6pnAyc1c/zLgOcn+ezklrTtqmpj834b8EV2/DtPDwPDfUexl9ELjx2CYaFWzQnhC4AfVtXHJruebZVkepJHNcuPAI4HfjS5VW29qnp3Vc2oqtn07oLwzap63SSXtU2S7NNcTEEzVfNCYIe+urCqfg7cmuSpTdML6N2lYofQ5V1nd1lJLgaOAx6bZBg4p6oumNyqtsmzgf8KfL+Z5wf486paMYk1bYsnAhc2D9TaDbi0qnaKy013Io8Hvtj7dwq7A5+vqq9ObkkT4r8Dn2uuhNoAvGGS6xmYl85Kklo5DSVJamVYSJJaGRaSpFaGhSSplWEhSWplWGiXluTqJC8a0fb2JJ8c535WbP7txhh97tlC+2eSnDKOz/pEkvf1rb8nyeLBq5XGz99ZaFd3Mb0fsl3Z1zYfeOcgg5sfLKaqXtJBbVvyXmBNks/Ru3/Sn9C7X5fUGY8stKu7DHhpkr3gdzdKfBJwXZJ9k3wjyQ3NcxVO3tyneRbBJ4EbgJnNsxce22y/orn53dqRN8BL8tFmf99IMn1kMUmOSnJNM/7K5vbwD9Hcl+s9wN8Bi4Gzd6S7l2rHZFhol1ZVdwDf5cF7Q80HLqner1X/A3hFczO75wEfbY4kAJ5K73klR1bVT0bs9o1VdRS9Z0u8LcljmvZ9gBua/V0DnNM/qLn/1t8CpzTjlwIf2ELdFwMH0Ht2xUVb+fWlgTkNJT04FfW/mvc3Nu0B/qq52+kD9J7h8fhm20/GeFjS25K8olmeCcwF7mj2cUnT/llg5A0ZnwocDlzVZNI04GejfUDz/IonAJVk377nc0idMCwkuAL4WJJnAI/Y/KAn4I+B6cBRVfXb5q6uezfb7h1tR0mOo3djwmdV1a+SXN03ZqSR99oJsLaqBnnU5seB/wE8jd4RykDnWKSt5TSUdnnNv8qvpjftc3Hfpv3pPSfit0meBxw0wO72B+5qguIQ4A/7tu0GbL7q6bX0Hufabx0wffNzmZPskeSwkR+Q5MXA44B/BN4PvCLJoQPUJm01w0LquRj4A3rPg9jsc8BQklX0jjIGuY35V4Hdk3yP3l/k/VNV9wKHJVkNPB9Y1D+wqu6jFyYfTPIvwBrgP/f3SbI3vafivbV5POy99J6Q93eDflFpa3jXWUlSK48sJEmtDAtJUivDQpLUyrCQJLUyLCRJrQwLSVIrw0KS1Or/A/TsX+z0WNprAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array([1, 2, 3, 4, 5, 6])\n",
    "y = np.array([0.5/6, 1/6, 1.5/6, 0.5/6, 2/6, 1/6])\n",
    "plt.bar(x, y)\n",
    "plt.axvline(np.dot(x, y), c='r')\n",
    "plt.annotate('X = %.2f' %np.dot(x, y), xy=(3.2, 0.3), color='r')\n",
    "plt.xlabel('Variable X')\n",
    "plt.ylabel('Probability')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Unnamed: 0</th>\n",
       "      <th>parent</th>\n",
       "      <th>child</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1</td>\n",
       "      <td>70.5</td>\n",
       "      <td>61.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>2</td>\n",
       "      <td>68.5</td>\n",
       "      <td>61.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>3</td>\n",
       "      <td>65.5</td>\n",
       "      <td>61.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4</td>\n",
       "      <td>64.5</td>\n",
       "      <td>61.7</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5</td>\n",
       "      <td>64.0</td>\n",
       "      <td>61.7</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Unnamed: 0  parent  child\n",
       "0           1    70.5   61.7\n",
       "1           2    68.5   61.7\n",
       "2           3    65.5   61.7\n",
       "3           4    64.5   61.7\n",
       "4           5    64.0   61.7"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# work with pandas dataframes - basics\n",
    "# https://medium.com/dunder-data/selecting-subsets-of-data-in-pandas-6fcd0170be9c\n",
    "df = pd.read_csv('galton.csv')\n",
    "df.head()\n",
    "#df['parent'].head().values\n",
    "#df['parent'].head().index"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "# https://www.rapidtables.com/web/color/RGB_Color.html#color-table\n",
    "# https://jakevdp.github.io/PythonDataScienceHandbook/04.08-multiple-subplots.html\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.mlab as mlab\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "\n",
    "xc = df['child'].values\n",
    "mu, sigma = stats.norm.fit(xc)\n",
    "\n",
    "xp = df['parent'].values\n",
    "mu_p, sigma_p = stats.norm.fit(xp)\n",
    "\n",
    "fig = plt.figure(figsize=(10, 5))\n",
    "ax1 = fig.add_subplot(1, 2, 1)\n",
    "ax2 = fig.add_subplot(1, 2, 2)\n",
    "\n",
    "# the histogram of the data\n",
    "n, bins, patches = ax1.hist(xc, 12, rwidth=0.9, density=True, facecolor='coral', alpha=0.75)\n",
    "n_p, bins_p, patches_p = ax2.hist(xp, 9, rwidth=0.9, density=True, facecolor='teal', alpha=0.75)\n",
    "\n",
    "# add a 'best fit' line\n",
    "y = stats.norm.pdf(bins, mu, sigma)\n",
    "l = ax1.plot(bins, y, 'k-', linewidth=2)\n",
    "y_p = stats.norm.pdf(bins_p, mu_p, sigma_p)\n",
    "l_p = ax2.plot(bins_p, y_p, 'k-', linewidth=2)\n",
    "\n",
    "ax1.set_xlabel('Variable')\n",
    "ax1.set_ylabel('Probability')\n",
    "ax1.set_title('Histogram of Children Height: \\n$\\mu$=' + '%.2f' % mu + ', $\\sigma$=' + '%.2f' % sigma)\n",
    "ax1.grid(True)\n",
    "\n",
    "ax2.set_xlabel('Variable')\n",
    "ax2.set_ylabel('Probability')\n",
    "ax2.set_title('Histogram of Parents Height: \\n$\\mu$=' + '%.2f' % mu_p + ', $\\sigma$=' + '%.2f' % sigma_p)\n",
    "ax2.grid(True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "application/javascript": [
       "/* Put everything inside the global mpl namespace */\n",
       "window.mpl = {};\n",
       "\n",
       "\n",
       "mpl.get_websocket_type = function() {\n",
       "    if (typeof(WebSocket) !== 'undefined') {\n",
       "        return WebSocket;\n",
       "    } else if (typeof(MozWebSocket) !== 'undefined') {\n",
       "        return MozWebSocket;\n",
       "    } else {\n",
       "        alert('Your browser does not have WebSocket support.' +\n",
       "              'Please try Chrome, Safari or Firefox ≥ 6. ' +\n",
       "              'Firefox 4 and 5 are also supported but you ' +\n",
       "              'have to enable WebSockets in about:config.');\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure = function(figure_id, websocket, ondownload, parent_element) {\n",
       "    this.id = figure_id;\n",
       "\n",
       "    this.ws = websocket;\n",
       "\n",
       "    this.supports_binary = (this.ws.binaryType != undefined);\n",
       "\n",
       "    if (!this.supports_binary) {\n",
       "        var warnings = document.getElementById(\"mpl-warnings\");\n",
       "        if (warnings) {\n",
       "            warnings.style.display = 'block';\n",
       "            warnings.textContent = (\n",
       "                \"This browser does not support binary websocket messages. \" +\n",
       "                    \"Performance may be slow.\");\n",
       "        }\n",
       "    }\n",
       "\n",
       "    this.imageObj = new Image();\n",
       "\n",
       "    this.context = undefined;\n",
       "    this.message = undefined;\n",
       "    this.canvas = undefined;\n",
       "    this.rubberband_canvas = undefined;\n",
       "    this.rubberband_context = undefined;\n",
       "    this.format_dropdown = undefined;\n",
       "\n",
       "    this.image_mode = 'full';\n",
       "\n",
       "    this.root = $('<div/>');\n",
       "    this._root_extra_style(this.root)\n",
       "    this.root.attr('style', 'display: inline-block');\n",
       "\n",
       "    $(parent_element).append(this.root);\n",
       "\n",
       "    this._init_header(this);\n",
       "    this._init_canvas(this);\n",
       "    this._init_toolbar(this);\n",
       "\n",
       "    var fig = this;\n",
       "\n",
       "    this.waiting = false;\n",
       "\n",
       "    this.ws.onopen =  function () {\n",
       "            fig.send_message(\"supports_binary\", {value: fig.supports_binary});\n",
       "            fig.send_message(\"send_image_mode\", {});\n",
       "            if (mpl.ratio != 1) {\n",
       "                fig.send_message(\"set_dpi_ratio\", {'dpi_ratio': mpl.ratio});\n",
       "            }\n",
       "            fig.send_message(\"refresh\", {});\n",
       "        }\n",
       "\n",
       "    this.imageObj.onload = function() {\n",
       "            if (fig.image_mode == 'full') {\n",
       "                // Full images could contain transparency (where diff images\n",
       "                // almost always do), so we need to clear the canvas so that\n",
       "                // there is no ghosting.\n",
       "                fig.context.clearRect(0, 0, fig.canvas.width, fig.canvas.height);\n",
       "            }\n",
       "            fig.context.drawImage(fig.imageObj, 0, 0);\n",
       "        };\n",
       "\n",
       "    this.imageObj.onunload = function() {\n",
       "        fig.ws.close();\n",
       "    }\n",
       "\n",
       "    this.ws.onmessage = this._make_on_message_function(this);\n",
       "\n",
       "    this.ondownload = ondownload;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_header = function() {\n",
       "    var titlebar = $(\n",
       "        '<div class=\"ui-dialog-titlebar ui-widget-header ui-corner-all ' +\n",
       "        'ui-helper-clearfix\"/>');\n",
       "    var titletext = $(\n",
       "        '<div class=\"ui-dialog-title\" style=\"width: 100%; ' +\n",
       "        'text-align: center; padding: 3px;\"/>');\n",
       "    titlebar.append(titletext)\n",
       "    this.root.append(titlebar);\n",
       "    this.header = titletext[0];\n",
       "}\n",
       "\n",
       "\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(canvas_div) {\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_canvas = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var canvas_div = $('<div/>');\n",
       "\n",
       "    canvas_div.attr('style', 'position: relative; clear: both; outline: 0');\n",
       "\n",
       "    function canvas_keyboard_event(event) {\n",
       "        return fig.key_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    canvas_div.keydown('key_press', canvas_keyboard_event);\n",
       "    canvas_div.keyup('key_release', canvas_keyboard_event);\n",
       "    this.canvas_div = canvas_div\n",
       "    this._canvas_extra_style(canvas_div)\n",
       "    this.root.append(canvas_div);\n",
       "\n",
       "    var canvas = $('<canvas/>');\n",
       "    canvas.addClass('mpl-canvas');\n",
       "    canvas.attr('style', \"left: 0; top: 0; z-index: 0; outline: 0\")\n",
       "\n",
       "    this.canvas = canvas[0];\n",
       "    this.context = canvas[0].getContext(\"2d\");\n",
       "\n",
       "    var backingStore = this.context.backingStorePixelRatio ||\n",
       "\tthis.context.webkitBackingStorePixelRatio ||\n",
       "\tthis.context.mozBackingStorePixelRatio ||\n",
       "\tthis.context.msBackingStorePixelRatio ||\n",
       "\tthis.context.oBackingStorePixelRatio ||\n",
       "\tthis.context.backingStorePixelRatio || 1;\n",
       "\n",
       "    mpl.ratio = (window.devicePixelRatio || 1) / backingStore;\n",
       "\n",
       "    var rubberband = $('<canvas/>');\n",
       "    rubberband.attr('style', \"position: absolute; left: 0; top: 0; z-index: 1;\")\n",
       "\n",
       "    var pass_mouse_events = true;\n",
       "\n",
       "    canvas_div.resizable({\n",
       "        start: function(event, ui) {\n",
       "            pass_mouse_events = false;\n",
       "        },\n",
       "        resize: function(event, ui) {\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "        stop: function(event, ui) {\n",
       "            pass_mouse_events = true;\n",
       "            fig.request_resize(ui.size.width, ui.size.height);\n",
       "        },\n",
       "    });\n",
       "\n",
       "    function mouse_event_fn(event) {\n",
       "        if (pass_mouse_events)\n",
       "            return fig.mouse_event(event, event['data']);\n",
       "    }\n",
       "\n",
       "    rubberband.mousedown('button_press', mouse_event_fn);\n",
       "    rubberband.mouseup('button_release', mouse_event_fn);\n",
       "    // Throttle sequential mouse events to 1 every 20ms.\n",
       "    rubberband.mousemove('motion_notify', mouse_event_fn);\n",
       "\n",
       "    rubberband.mouseenter('figure_enter', mouse_event_fn);\n",
       "    rubberband.mouseleave('figure_leave', mouse_event_fn);\n",
       "\n",
       "    canvas_div.on(\"wheel\", function (event) {\n",
       "        event = event.originalEvent;\n",
       "        event['data'] = 'scroll'\n",
       "        if (event.deltaY < 0) {\n",
       "            event.step = 1;\n",
       "        } else {\n",
       "            event.step = -1;\n",
       "        }\n",
       "        mouse_event_fn(event);\n",
       "    });\n",
       "\n",
       "    canvas_div.append(canvas);\n",
       "    canvas_div.append(rubberband);\n",
       "\n",
       "    this.rubberband = rubberband;\n",
       "    this.rubberband_canvas = rubberband[0];\n",
       "    this.rubberband_context = rubberband[0].getContext(\"2d\");\n",
       "    this.rubberband_context.strokeStyle = \"#000000\";\n",
       "\n",
       "    this._resize_canvas = function(width, height) {\n",
       "        // Keep the size of the canvas, canvas container, and rubber band\n",
       "        // canvas in synch.\n",
       "        canvas_div.css('width', width)\n",
       "        canvas_div.css('height', height)\n",
       "\n",
       "        canvas.attr('width', width * mpl.ratio);\n",
       "        canvas.attr('height', height * mpl.ratio);\n",
       "        canvas.attr('style', 'width: ' + width + 'px; height: ' + height + 'px;');\n",
       "\n",
       "        rubberband.attr('width', width);\n",
       "        rubberband.attr('height', height);\n",
       "    }\n",
       "\n",
       "    // Set the figure to an initial 600x600px, this will subsequently be updated\n",
       "    // upon first draw.\n",
       "    this._resize_canvas(600, 600);\n",
       "\n",
       "    // Disable right mouse context menu.\n",
       "    $(this.rubberband_canvas).bind(\"contextmenu\",function(e){\n",
       "        return false;\n",
       "    });\n",
       "\n",
       "    function set_focus () {\n",
       "        canvas.focus();\n",
       "        canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    window.setTimeout(set_focus, 100);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items) {\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) {\n",
       "            // put a spacer in here.\n",
       "            continue;\n",
       "        }\n",
       "        var button = $('<button/>');\n",
       "        button.addClass('ui-button ui-widget ui-state-default ui-corner-all ' +\n",
       "                        'ui-button-icon-only');\n",
       "        button.attr('role', 'button');\n",
       "        button.attr('aria-disabled', 'false');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "\n",
       "        var icon_img = $('<span/>');\n",
       "        icon_img.addClass('ui-button-icon-primary ui-icon');\n",
       "        icon_img.addClass(image);\n",
       "        icon_img.addClass('ui-corner-all');\n",
       "\n",
       "        var tooltip_span = $('<span/>');\n",
       "        tooltip_span.addClass('ui-button-text');\n",
       "        tooltip_span.html(tooltip);\n",
       "\n",
       "        button.append(icon_img);\n",
       "        button.append(tooltip_span);\n",
       "\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    var fmt_picker_span = $('<span/>');\n",
       "\n",
       "    var fmt_picker = $('<select/>');\n",
       "    fmt_picker.addClass('mpl-toolbar-option ui-widget ui-widget-content');\n",
       "    fmt_picker_span.append(fmt_picker);\n",
       "    nav_element.append(fmt_picker_span);\n",
       "    this.format_dropdown = fmt_picker[0];\n",
       "\n",
       "    for (var ind in mpl.extensions) {\n",
       "        var fmt = mpl.extensions[ind];\n",
       "        var option = $(\n",
       "            '<option/>', {selected: fmt === mpl.default_extension}).html(fmt);\n",
       "        fmt_picker.append(option)\n",
       "    }\n",
       "\n",
       "    // Add hover states to the ui-buttons\n",
       "    $( \".ui-button\" ).hover(\n",
       "        function() { $(this).addClass(\"ui-state-hover\");},\n",
       "        function() { $(this).removeClass(\"ui-state-hover\");}\n",
       "    );\n",
       "\n",
       "    var status_bar = $('<span class=\"mpl-message\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.request_resize = function(x_pixels, y_pixels) {\n",
       "    // Request matplotlib to resize the figure. Matplotlib will then trigger a resize in the client,\n",
       "    // which will in turn request a refresh of the image.\n",
       "    this.send_message('resize', {'width': x_pixels, 'height': y_pixels});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_message = function(type, properties) {\n",
       "    properties['type'] = type;\n",
       "    properties['figure_id'] = this.id;\n",
       "    this.ws.send(JSON.stringify(properties));\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.send_draw_message = function() {\n",
       "    if (!this.waiting) {\n",
       "        this.waiting = true;\n",
       "        this.ws.send(JSON.stringify({type: \"draw\", figure_id: this.id}));\n",
       "    }\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    var format_dropdown = fig.format_dropdown;\n",
       "    var format = format_dropdown.options[format_dropdown.selectedIndex].value;\n",
       "    fig.ondownload(fig, format);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.figure.prototype.handle_resize = function(fig, msg) {\n",
       "    var size = msg['size'];\n",
       "    if (size[0] != fig.canvas.width || size[1] != fig.canvas.height) {\n",
       "        fig._resize_canvas(size[0], size[1]);\n",
       "        fig.send_message(\"refresh\", {});\n",
       "    };\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_rubberband = function(fig, msg) {\n",
       "    var x0 = msg['x0'] / mpl.ratio;\n",
       "    var y0 = (fig.canvas.height - msg['y0']) / mpl.ratio;\n",
       "    var x1 = msg['x1'] / mpl.ratio;\n",
       "    var y1 = (fig.canvas.height - msg['y1']) / mpl.ratio;\n",
       "    x0 = Math.floor(x0) + 0.5;\n",
       "    y0 = Math.floor(y0) + 0.5;\n",
       "    x1 = Math.floor(x1) + 0.5;\n",
       "    y1 = Math.floor(y1) + 0.5;\n",
       "    var min_x = Math.min(x0, x1);\n",
       "    var min_y = Math.min(y0, y1);\n",
       "    var width = Math.abs(x1 - x0);\n",
       "    var height = Math.abs(y1 - y0);\n",
       "\n",
       "    fig.rubberband_context.clearRect(\n",
       "        0, 0, fig.canvas.width, fig.canvas.height);\n",
       "\n",
       "    fig.rubberband_context.strokeRect(min_x, min_y, width, height);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_figure_label = function(fig, msg) {\n",
       "    // Updates the figure title.\n",
       "    fig.header.textContent = msg['label'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_cursor = function(fig, msg) {\n",
       "    var cursor = msg['cursor'];\n",
       "    switch(cursor)\n",
       "    {\n",
       "    case 0:\n",
       "        cursor = 'pointer';\n",
       "        break;\n",
       "    case 1:\n",
       "        cursor = 'default';\n",
       "        break;\n",
       "    case 2:\n",
       "        cursor = 'crosshair';\n",
       "        break;\n",
       "    case 3:\n",
       "        cursor = 'move';\n",
       "        break;\n",
       "    }\n",
       "    fig.rubberband_canvas.style.cursor = cursor;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_message = function(fig, msg) {\n",
       "    fig.message.textContent = msg['message'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_draw = function(fig, msg) {\n",
       "    // Request the server to send over a new figure.\n",
       "    fig.send_draw_message();\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_image_mode = function(fig, msg) {\n",
       "    fig.image_mode = msg['mode'];\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Called whenever the canvas gets updated.\n",
       "    this.send_message(\"ack\", {});\n",
       "}\n",
       "\n",
       "// A function to construct a web socket function for onmessage handling.\n",
       "// Called in the figure constructor.\n",
       "mpl.figure.prototype._make_on_message_function = function(fig) {\n",
       "    return function socket_on_message(evt) {\n",
       "        if (evt.data instanceof Blob) {\n",
       "            /* FIXME: We get \"Resource interpreted as Image but\n",
       "             * transferred with MIME type text/plain:\" errors on\n",
       "             * Chrome.  But how to set the MIME type?  It doesn't seem\n",
       "             * to be part of the websocket stream */\n",
       "            evt.data.type = \"image/png\";\n",
       "\n",
       "            /* Free the memory for the previous frames */\n",
       "            if (fig.imageObj.src) {\n",
       "                (window.URL || window.webkitURL).revokeObjectURL(\n",
       "                    fig.imageObj.src);\n",
       "            }\n",
       "\n",
       "            fig.imageObj.src = (window.URL || window.webkitURL).createObjectURL(\n",
       "                evt.data);\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "        else if (typeof evt.data === 'string' && evt.data.slice(0, 21) == \"data:image/png;base64\") {\n",
       "            fig.imageObj.src = evt.data;\n",
       "            fig.updated_canvas_event();\n",
       "            fig.waiting = false;\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        var msg = JSON.parse(evt.data);\n",
       "        var msg_type = msg['type'];\n",
       "\n",
       "        // Call the  \"handle_{type}\" callback, which takes\n",
       "        // the figure and JSON message as its only arguments.\n",
       "        try {\n",
       "            var callback = fig[\"handle_\" + msg_type];\n",
       "        } catch (e) {\n",
       "            console.log(\"No handler for the '\" + msg_type + \"' message type: \", msg);\n",
       "            return;\n",
       "        }\n",
       "\n",
       "        if (callback) {\n",
       "            try {\n",
       "                // console.log(\"Handling '\" + msg_type + \"' message: \", msg);\n",
       "                callback(fig, msg);\n",
       "            } catch (e) {\n",
       "                console.log(\"Exception inside the 'handler_\" + msg_type + \"' callback:\", e, e.stack, msg);\n",
       "            }\n",
       "        }\n",
       "    };\n",
       "}\n",
       "\n",
       "// from http://stackoverflow.com/questions/1114465/getting-mouse-location-in-canvas\n",
       "mpl.findpos = function(e) {\n",
       "    //this section is from http://www.quirksmode.org/js/events_properties.html\n",
       "    var targ;\n",
       "    if (!e)\n",
       "        e = window.event;\n",
       "    if (e.target)\n",
       "        targ = e.target;\n",
       "    else if (e.srcElement)\n",
       "        targ = e.srcElement;\n",
       "    if (targ.nodeType == 3) // defeat Safari bug\n",
       "        targ = targ.parentNode;\n",
       "\n",
       "    // jQuery normalizes the pageX and pageY\n",
       "    // pageX,Y are the mouse positions relative to the document\n",
       "    // offset() returns the position of the element relative to the document\n",
       "    var x = e.pageX - $(targ).offset().left;\n",
       "    var y = e.pageY - $(targ).offset().top;\n",
       "\n",
       "    return {\"x\": x, \"y\": y};\n",
       "};\n",
       "\n",
       "/*\n",
       " * return a copy of an object with only non-object keys\n",
       " * we need this to avoid circular references\n",
       " * http://stackoverflow.com/a/24161582/3208463\n",
       " */\n",
       "function simpleKeys (original) {\n",
       "  return Object.keys(original).reduce(function (obj, key) {\n",
       "    if (typeof original[key] !== 'object')\n",
       "        obj[key] = original[key]\n",
       "    return obj;\n",
       "  }, {});\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.mouse_event = function(event, name) {\n",
       "    var canvas_pos = mpl.findpos(event)\n",
       "\n",
       "    if (name === 'button_press')\n",
       "    {\n",
       "        this.canvas.focus();\n",
       "        this.canvas_div.focus();\n",
       "    }\n",
       "\n",
       "    var x = canvas_pos.x * mpl.ratio;\n",
       "    var y = canvas_pos.y * mpl.ratio;\n",
       "\n",
       "    this.send_message(name, {x: x, y: y, button: event.button,\n",
       "                             step: event.step,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "\n",
       "    /* This prevents the web browser from automatically changing to\n",
       "     * the text insertion cursor when the button is pressed.  We want\n",
       "     * to control all of the cursor setting manually through the\n",
       "     * 'cursor' event from matplotlib */\n",
       "    event.preventDefault();\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    // Handle any extra behaviour associated with a key event\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.key_event = function(event, name) {\n",
       "\n",
       "    // Prevent repeat events\n",
       "    if (name == 'key_press')\n",
       "    {\n",
       "        if (event.which === this._key)\n",
       "            return;\n",
       "        else\n",
       "            this._key = event.which;\n",
       "    }\n",
       "    if (name == 'key_release')\n",
       "        this._key = null;\n",
       "\n",
       "    var value = '';\n",
       "    if (event.ctrlKey && event.which != 17)\n",
       "        value += \"ctrl+\";\n",
       "    if (event.altKey && event.which != 18)\n",
       "        value += \"alt+\";\n",
       "    if (event.shiftKey && event.which != 16)\n",
       "        value += \"shift+\";\n",
       "\n",
       "    value += 'k';\n",
       "    value += event.which.toString();\n",
       "\n",
       "    this._key_event_extra(event, name);\n",
       "\n",
       "    this.send_message(name, {key: value,\n",
       "                             guiEvent: simpleKeys(event)});\n",
       "    return false;\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onclick = function(name) {\n",
       "    if (name == 'download') {\n",
       "        this.handle_save(this, null);\n",
       "    } else {\n",
       "        this.send_message(\"toolbar_button\", {name: name});\n",
       "    }\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.toolbar_button_onmouseover = function(tooltip) {\n",
       "    this.message.textContent = tooltip;\n",
       "};\n",
       "mpl.toolbar_items = [[\"Home\", \"Reset original view\", \"fa fa-home icon-home\", \"home\"], [\"Back\", \"Back to previous view\", \"fa fa-arrow-left icon-arrow-left\", \"back\"], [\"Forward\", \"Forward to next view\", \"fa fa-arrow-right icon-arrow-right\", \"forward\"], [\"\", \"\", \"\", \"\"], [\"Pan\", \"Pan axes with left mouse, zoom with right\", \"fa fa-arrows icon-move\", \"pan\"], [\"Zoom\", \"Zoom to rectangle\", \"fa fa-square-o icon-check-empty\", \"zoom\"], [\"\", \"\", \"\", \"\"], [\"Download\", \"Download plot\", \"fa fa-floppy-o icon-save\", \"download\"]];\n",
       "\n",
       "mpl.extensions = [\"eps\", \"jpeg\", \"pdf\", \"png\", \"ps\", \"raw\", \"svg\", \"tif\"];\n",
       "\n",
       "mpl.default_extension = \"png\";var comm_websocket_adapter = function(comm) {\n",
       "    // Create a \"websocket\"-like object which calls the given IPython comm\n",
       "    // object with the appropriate methods. Currently this is a non binary\n",
       "    // socket, so there is still some room for performance tuning.\n",
       "    var ws = {};\n",
       "\n",
       "    ws.close = function() {\n",
       "        comm.close()\n",
       "    };\n",
       "    ws.send = function(m) {\n",
       "        //console.log('sending', m);\n",
       "        comm.send(m);\n",
       "    };\n",
       "    // Register the callback with on_msg.\n",
       "    comm.on_msg(function(msg) {\n",
       "        //console.log('receiving', msg['content']['data'], msg);\n",
       "        // Pass the mpl event to the overridden (by mpl) onmessage function.\n",
       "        ws.onmessage(msg['content']['data'])\n",
       "    });\n",
       "    return ws;\n",
       "}\n",
       "\n",
       "mpl.mpl_figure_comm = function(comm, msg) {\n",
       "    // This is the function which gets called when the mpl process\n",
       "    // starts-up an IPython Comm through the \"matplotlib\" channel.\n",
       "\n",
       "    var id = msg.content.data.id;\n",
       "    // Get hold of the div created by the display call when the Comm\n",
       "    // socket was opened in Python.\n",
       "    var element = $(\"#\" + id);\n",
       "    var ws_proxy = comm_websocket_adapter(comm)\n",
       "\n",
       "    function ondownload(figure, format) {\n",
       "        window.open(figure.imageObj.src);\n",
       "    }\n",
       "\n",
       "    var fig = new mpl.figure(id, ws_proxy,\n",
       "                           ondownload,\n",
       "                           element.get(0));\n",
       "\n",
       "    // Call onopen now - mpl needs it, as it is assuming we've passed it a real\n",
       "    // web socket which is closed, not our websocket->open comm proxy.\n",
       "    ws_proxy.onopen();\n",
       "\n",
       "    fig.parent_element = element.get(0);\n",
       "    fig.cell_info = mpl.find_output_cell(\"<div id='\" + id + \"'></div>\");\n",
       "    if (!fig.cell_info) {\n",
       "        console.error(\"Failed to find cell for figure\", id, fig);\n",
       "        return;\n",
       "    }\n",
       "\n",
       "    var output_index = fig.cell_info[2]\n",
       "    var cell = fig.cell_info[0];\n",
       "\n",
       "};\n",
       "\n",
       "mpl.figure.prototype.handle_close = function(fig, msg) {\n",
       "    var width = fig.canvas.width/mpl.ratio\n",
       "    fig.root.unbind('remove')\n",
       "\n",
       "    // Update the output cell to use the data from the current canvas.\n",
       "    fig.push_to_output();\n",
       "    var dataURL = fig.canvas.toDataURL();\n",
       "    // Re-enable the keyboard manager in IPython - without this line, in FF,\n",
       "    // the notebook keyboard shortcuts fail.\n",
       "    IPython.keyboard_manager.enable()\n",
       "    $(fig.parent_element).html('<img src=\"' + dataURL + '\" width=\"' + width + '\">');\n",
       "    fig.close_ws(fig, msg);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.close_ws = function(fig, msg){\n",
       "    fig.send_message('closing', msg);\n",
       "    // fig.ws.close()\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.push_to_output = function(remove_interactive) {\n",
       "    // Turn the data on the canvas into data in the output cell.\n",
       "    var width = this.canvas.width/mpl.ratio\n",
       "    var dataURL = this.canvas.toDataURL();\n",
       "    this.cell_info[1]['text/html'] = '<img src=\"' + dataURL + '\" width=\"' + width + '\">';\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.updated_canvas_event = function() {\n",
       "    // Tell IPython that the notebook contents must change.\n",
       "    IPython.notebook.set_dirty(true);\n",
       "    this.send_message(\"ack\", {});\n",
       "    var fig = this;\n",
       "    // Wait a second, then push the new image to the DOM so\n",
       "    // that it is saved nicely (might be nice to debounce this).\n",
       "    setTimeout(function () { fig.push_to_output() }, 1000);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._init_toolbar = function() {\n",
       "    var fig = this;\n",
       "\n",
       "    var nav_element = $('<div/>')\n",
       "    nav_element.attr('style', 'width: 100%');\n",
       "    this.root.append(nav_element);\n",
       "\n",
       "    // Define a callback function for later on.\n",
       "    function toolbar_event(event) {\n",
       "        return fig.toolbar_button_onclick(event['data']);\n",
       "    }\n",
       "    function toolbar_mouse_event(event) {\n",
       "        return fig.toolbar_button_onmouseover(event['data']);\n",
       "    }\n",
       "\n",
       "    for(var toolbar_ind in mpl.toolbar_items){\n",
       "        var name = mpl.toolbar_items[toolbar_ind][0];\n",
       "        var tooltip = mpl.toolbar_items[toolbar_ind][1];\n",
       "        var image = mpl.toolbar_items[toolbar_ind][2];\n",
       "        var method_name = mpl.toolbar_items[toolbar_ind][3];\n",
       "\n",
       "        if (!name) { continue; };\n",
       "\n",
       "        var button = $('<button class=\"btn btn-default\" href=\"#\" title=\"' + name + '\"><i class=\"fa ' + image + ' fa-lg\"></i></button>');\n",
       "        button.click(method_name, toolbar_event);\n",
       "        button.mouseover(tooltip, toolbar_mouse_event);\n",
       "        nav_element.append(button);\n",
       "    }\n",
       "\n",
       "    // Add the status bar.\n",
       "    var status_bar = $('<span class=\"mpl-message\" style=\"text-align:right; float: right;\"/>');\n",
       "    nav_element.append(status_bar);\n",
       "    this.message = status_bar[0];\n",
       "\n",
       "    // Add the close button to the window.\n",
       "    var buttongrp = $('<div class=\"btn-group inline pull-right\"></div>');\n",
       "    var button = $('<button class=\"btn btn-mini btn-primary\" href=\"#\" title=\"Stop Interaction\"><i class=\"fa fa-power-off icon-remove icon-large\"></i></button>');\n",
       "    button.click(function (evt) { fig.handle_close(fig, {}); } );\n",
       "    button.mouseover('Stop Interaction', toolbar_mouse_event);\n",
       "    buttongrp.append(button);\n",
       "    var titlebar = this.root.find($('.ui-dialog-titlebar'));\n",
       "    titlebar.prepend(buttongrp);\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._root_extra_style = function(el){\n",
       "    var fig = this\n",
       "    el.on(\"remove\", function(){\n",
       "\tfig.close_ws(fig, {});\n",
       "    });\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._canvas_extra_style = function(el){\n",
       "    // this is important to make the div 'focusable\n",
       "    el.attr('tabindex', 0)\n",
       "    // reach out to IPython and tell the keyboard manager to turn it's self\n",
       "    // off when our div gets focus\n",
       "\n",
       "    // location in version 3\n",
       "    if (IPython.notebook.keyboard_manager) {\n",
       "        IPython.notebook.keyboard_manager.register_events(el);\n",
       "    }\n",
       "    else {\n",
       "        // location in version 2\n",
       "        IPython.keyboard_manager.register_events(el);\n",
       "    }\n",
       "\n",
       "}\n",
       "\n",
       "mpl.figure.prototype._key_event_extra = function(event, name) {\n",
       "    var manager = IPython.notebook.keyboard_manager;\n",
       "    if (!manager)\n",
       "        manager = IPython.keyboard_manager;\n",
       "\n",
       "    // Check for shift+enter\n",
       "    if (event.shiftKey && event.which == 13) {\n",
       "        this.canvas_div.blur();\n",
       "        event.shiftKey = false;\n",
       "        // Send a \"J\" for go to next cell\n",
       "        event.which = 74;\n",
       "        event.keyCode = 74;\n",
       "        manager.command_mode();\n",
       "        manager.handle_keydown(event);\n",
       "    }\n",
       "}\n",
       "\n",
       "mpl.figure.prototype.handle_save = function(fig, msg) {\n",
       "    fig.ondownload(fig, null);\n",
       "}\n",
       "\n",
       "\n",
       "mpl.find_output_cell = function(html_output) {\n",
       "    // Return the cell and output element which can be found *uniquely* in the notebook.\n",
       "    // Note - this is a bit hacky, but it is done because the \"notebook_saving.Notebook\"\n",
       "    // IPython event is triggered only after the cells have been serialised, which for\n",
       "    // our purposes (turning an active figure into a static one), is too late.\n",
       "    var cells = IPython.notebook.get_cells();\n",
       "    var ncells = cells.length;\n",
       "    for (var i=0; i<ncells; i++) {\n",
       "        var cell = cells[i];\n",
       "        if (cell.cell_type === 'code'){\n",
       "            for (var j=0; j<cell.output_area.outputs.length; j++) {\n",
       "                var data = cell.output_area.outputs[j];\n",
       "                if (data.data) {\n",
       "                    // IPython >= 3 moved mimebundle to data attribute of output\n",
       "                    data = data.data;\n",
       "                }\n",
       "                if (data['text/html'] == html_output) {\n",
       "                    return [cell, data, j];\n",
       "                }\n",
       "            }\n",
       "        }\n",
       "    }\n",
       "}\n",
       "\n",
       "// Register the function which deals with the matplotlib target/channel.\n",
       "// The kernel may be null if the page has been refreshed.\n",
       "if (IPython.notebook.kernel != null) {\n",
       "    IPython.notebook.kernel.comm_manager.register_target('matplotlib', mpl.mpl_figure_comm);\n",
       "}\n"
      ],
      "text/plain": [
       "<IPython.core.display.Javascript object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
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\" width=\"640\">"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "2de26352edad4c07a6e9e4710788f016",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "interactive(children=(FloatSlider(value=64.08846982758622, description='x', max=192.26540948275868, min=-64.08…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# pip install ipywidgets (in prealabil)\n",
    "# jupyter nbextension enable --py --sys-prefix widgetsnbextension (cu sudo)\n",
    "#\n",
    "# reopen page and run this frame first\n",
    "\n",
    "%matplotlib notebook\n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.mlab as mlab\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats as stats\n",
    "import pandas as pd\n",
    "from ipywidgets import *\n",
    "\n",
    "df = pd.read_csv('galton.csv')\n",
    "\n",
    "x = df['child'].values\n",
    "mu, sigma = stats.norm.fit(x)\n",
    "avg = np.average(x)\n",
    "\n",
    "# the histogram of the data\n",
    "n, bins, patches = plt.hist(x, 12, rwidth=0.95, density=True, facecolor='coral', alpha=0.75)\n",
    "\n",
    "# add a 'best fit' line\n",
    "y = stats.norm.pdf(bins, mu, sigma)\n",
    "l = plt.plot(bins, y, 'k-', linewidth=2)\n",
    "line = plt.axvline(x=mu, c='k', linestyle='--')\n",
    "label = plt.xlabel('Variable, ' + 'mean: %.2f' % mu + ' RMSE: %.2f' % (mu - avg)**2)\n",
    "plt.ylabel('Probability')\n",
    "plt.title(r'$\\mathrm{Histogram\\ of\\ Height:}\\ \\mu=' + '%.2f' % mu + ',\\ \\sigma=' + '%.2f' % sigma + '$')\n",
    "plt.grid(True)\n",
    "\n",
    "plt.show()\n",
    "\n",
    "def update(x = mu - 4):\n",
    "    line.set_xdata(x)\n",
    "    label.set_text('Variable, ' + 'mean: %.2f' % x + ' MSE: %.2f' % (x - avg)**2)\n",
    "    #plt.canvas.draw()\n",
    "\n",
    "interact(update);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "x = np.array([0, 1])\n",
    "y = np.array([.5, .5])\n",
    "fig = plt.figure(figsize=(10, 2))\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.bar(x, y)\n",
    "ax.axvline(np.dot(x, y), c='r')\n",
    "ax.set_xlabel('Variable X')\n",
    "ax.set_ylabel('Probability')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 720x144 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline\n",
    "\n",
    "x = np.array(range(1, 7))\n",
    "y = np.array([1/6] * 6)\n",
    "fig = plt.figure(figsize=(10, 2))\n",
    "ax = fig.add_subplot(1, 1, 1)\n",
    "ax.bar(x, y)\n",
    "ax.axvline(np.dot(x, y), c='r')\n",
    "ax.set_xlabel('Variable X, E[X] = %.2f' % np.dot(x, y))\n",
    "ax.set_ylabel('Probability')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.array([-.5, 0, 0, 1, 1, 1.5])\n",
    "y = np.array([0, 0, 1, 1, 0, 0])\n",
    "plt.plot(x, y, 'k', linewidth=2)\n",
    "plt.xlabel('Variable')\n",
    "plt.ylabel('Probability')\n",
    "plt.title('Uniform density')\n",
    "plt.axvline(.5, c='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def roll(n):\n",
    "    # construim o matrice de n x 10000 de valori aleatoare cuprinse intre 1 si 6\n",
    "    r = np.random.randint(1, high=7, size=(10000, n))\n",
    "    \n",
    "    # se face media doar pe axa 1, adica pe linii, rezultatul va fi o matrice\n",
    "    # de n x 1 in care fiecare element va fi media (aritmetica) a liniei anterioare\n",
    "    return np.average(r, axis=1)\n",
    "\n",
    "fig, (ax1, ax2, ax3, ax4) = plt.subplots(1, 4, sharey=True, figsize=(15, 5))\n",
    "kwargs = dict(rwidth=0.7, density=True, alpha=0.75, ec='k', linewidth=2)\n",
    "# schimbati scala cu density=True ca sa vedeti cum se reduce imprastierea mediei\n",
    "# si cum se 'ascute' gaussiana\n",
    "#\n",
    "# density=True schimba ordonata din valori count in valori relative, adica probabilitati,\n",
    "# deci considera ca toata histograma este o Probability Mass Function (si o reprezinta ca atare)\n",
    "#\n",
    "ax1.hist(roll(1), 6, **kwargs, facecolor='pink')\n",
    "[ax_.set_xlabel('x') for ax_ in [ax1, ax2, ax3, ax4]]\n",
    "ax1.set_ylabel('counts')\n",
    "ax2.hist(roll(2), 11, **kwargs, facecolor='teal')\n",
    "ax3.hist(roll(3), 16, **kwargs, facecolor='blue')\n",
    "ax4.hist(roll(4), 21, **kwargs, facecolor='magenta')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Variabilitate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "def roll(n):\n",
    "    r = np.random.randint(1, high=7, size=(10000, n))\n",
    "    \n",
    "    # dispersia se calculeaza ca mean(abs(x - x.mean())**2), unde \n",
    "    # mean(x) = x.sum() / N, cu N numarul de sample-uri\n",
    "    return np.var(r, axis=1, ddof=1)\n",
    "\n",
    "fig, (ax1, ax2, ax3) = plt.subplots(1, 3, sharey=True, figsize=(15, 5))\n",
    "kwargs = dict(rwidth=0.7, density=True, alpha=0.75, ec='k', linewidth=2)\n",
    "[ax_.set_xlabel('x') for ax_ in [ax1, ax2, ax3]]\n",
    "ax1.set_ylabel('Probability')\n",
    "\n",
    "ax1.hist(roll(10), 30, **kwargs, facecolor='pink')\n",
    "ax2.hist(roll(20), 30, **kwargs, facecolor='teal')\n",
    "ax3.hist(roll(40), 30, **kwargs, facecolor='blue')\n",
    "\n",
    "fig.legend(['10 aruncari', '20 aruncari', '40 aruncari'])\n",
    "[ax_.axvline(2.92, c='r') for ax_ in [ax1, ax2, ax3]]\n",
    "fig.suptitle('Distribuţia dispersiei sample-ului', fontsize=16)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.3148133292748816\n",
      "0.31622776601683794\n"
     ]
    }
   ],
   "source": [
    "nosim = 100000\n",
    "n = 10\n",
    "x = np.random.randn(nosim, n)\n",
    "x = np.mean(x, axis=1)\n",
    "print(np.std(x))\n",
    "print(1/np.sqrt(n))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.1579271981008971\n",
      "0.15811388300841897\n"
     ]
    }
   ],
   "source": [
    "nosim = 10000\n",
    "n = 10\n",
    "x = np.random.randint(low=0, high=2, size=(nosim, n))\n",
    "x = np.mean(x, axis=1)\n",
    "print(np.std(x))\n",
    "print(0.5/np.sqrt(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Laborator"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Valoare aşteptată (medie)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Valoarea aşteptată a unei variabile aleatoare X, E(X), este o măsură a tendinţei centrale a acesteia. Pentru o variabilă aleatoare X cu probability mass function PMF(X), valoarea aşteptată E(X) este definită ca suma peste toate valorile lui x, din x * p(x). E(x) reprezintă centrul de masă al unor 'bare de metal' poziţionate pe poziţiile x şi 'înalte' de valoarea p(x)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Un alt nume pentru valoarea aşteptată este media. De regulă, prin medie înţelegeam suma a n numere împărţită la n. Această definiţie este consistentă cu valoarea aşteptată E(X) pentru cazul în care toate numerele sunt echiprobabile (aceeaşi înălţime a 'barelor de oţel' de mai sus)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q1. Considerăm variabila aleatoare X care corespunde unei aruncări cu zarul. Dacă zarul este ideal (corect), toate feţele pot ieşi cu aceeaşi probabilitate. Care este valoarea aşteptată a lui X?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def q():\n",
    "    return 3.5\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(1, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q2. Presupunem că avem trei zaruri, primele două trucate, cu centrul de greutate diferit de mijloc, în timp ce al treilea este un zar ideal. Pentru fiecare din cele trei definim probability mass function caracteristică zarului:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "pmf1 = [0.04761905, 0.09523810, 0.14285714, 0.19047619, 0.23809524, 0.28571428]\n",
    "pmf2 = [0.28571429, 0.23809524, 0.19047619, 0.14285714, 0.09523810, 0.04761904]\n",
    "pmf3 = [0.16666666, 0.16666666, 0.16666667, 0.16666667, 0.16666667, 0.16666667]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Care este valoarea aşteptată pentru primul zar? Daţi răspunsul cu 4 zecimale. Definiţi funcţia expected() de mai jos. Verificaţi că aţi scris corect funcţia folosind valoarea aşteptată pentru un zar corect."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def expected(pmf):\n",
    "    lista=np.array([1,2,3,4,5,6])\n",
    "    return np.sum(np.multiply(pmf,lista))\n",
    "\n",
    "def q():\n",
    "    return round(expected(pmf1), 4)\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(2, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q3. Care este valoarea aşteptată pentru al doilea zar? (tot patru zecimale)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def q():\n",
    "    return round(expected(pmf2), 4)\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(3, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pentru două variabile aleatoare X1 şi X2, valoarea aşteptată a mediei lor se poate calcula ca media valorilor lor aşteptate. Aceasta datorită proprietăţii de liniaritate a valorii aşteptate:\n",
    "$E(\\alpha X_1 + \\beta X_2) = \\alpha E(X_1) + \\beta E(X_2)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q4. Care este valoarea aşteptată pentru media variabilelor aleatoare reprezentate de primele două zaruri?\n",
    "\n",
    "__Hint1__: funcţia zip(l1, l2) parcurge două liste prin construcţia de perechi cu elemente din ambele liste. \n",
    "Iteraţi de exemplu zip(range(3), range(1, 4)).\n",
    "\n",
    "__Hint2__: folosiţi funcţia round(x, 4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.4999999749999997\n",
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def q():\n",
    "    r=[(x + y)/2 for x, y in zip(pmf1, pmf2)]\n",
    "    r=expected(r)\n",
    "    return round(r,4)\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(4, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.linspace(-.5, 1.5, 200)\n",
    "y = np.logical_and(x >= 0, x <= 1)*1.0\n",
    "\n",
    "fig, (ax1, ax2) = plt.subplots(1, 2, figsize=(15, 5))\n",
    "ax1.plot(x, y)\n",
    "ax1.set_title('p(x)')\n",
    "ax2.plot(x, x*y)\n",
    "ax2.set_title('x * p(x)')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q5. Pentru densitatea de probabilitate f(x) dată mai sus, care este valoarea aşteptată pentru E(X)?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def q():\n",
    "    return 1\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(5, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q6. Mai jos este dată o populaţie de 6 numere, sub forma unui array Numpy. Funcţia Numpy mean() este folosită pentru a calcula media sa:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "valoarea aşteptată (media): 9.0\n"
     ]
    }
   ],
   "source": [
    "population = np.array([1, 4, 7, 10, 13, 19])\n",
    "print('valoarea aşteptată (media):', np.mean(population))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Mai departe, din această populaţie vom selecta, în mod aleator, un sample de trei valori. Vom face acest lucru de 1000 de ori (deci 1000 de sample-uri). Variabila $idx$ de mai jos descrie care din elementele populaţiei a fost selectat aleator - va fi o matrice de 1000 de linii x 3 coloane;"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 4 5]\n",
      " [1 4 5]\n",
      " [1 5 4]\n",
      " [3 1 0]\n",
      " [1 1 4]]\n"
     ]
    }
   ],
   "source": [
    "idx = np.random.randint(low=0, high=len(population), size=(1000, 3))\n",
    "\n",
    "# vedem primele 5 linii ale ei:\n",
    "print(idx[:5, :])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Folosind variabila $idx$, prin proiecţie pe populaţie, vom obţine cele 1000 de sample-uri (matricea rezultată are aceleaşi dimensiuni):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "forma matricii: (1000, 3) (linii, coloane)\n"
     ]
    }
   ],
   "source": [
    "samples = population[idx]\n",
    "print('forma matricii: %s (linii, coloane)' % str(samples.shape))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pentru fiecare linie, calculăm media (observaţi argumentul axis; acesta indică axa pentru care se face funcţia, aici 1 înseamnă că se face pe linii; pe coloane ar fi fost axis=0):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([13., 12., 12.,  5.,  7.])"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "means = np.mean(samples, axis=1)\n",
    "\n",
    "# iată primele 5 medii:\n",
    "means[:5]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Sample mean pe care o tot socotim de 1000 de ori are şi ea o distribuţie. Media acestei distribuţii este un estimator pentru media populaţiei:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.116"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(means)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Pentru dimensiuni ale sample-ului de 2, 3, 4, ridicaţi distribuţia sample mean, folosind atât codul de mai sus cât şi cel prezentat la curs pentru aruncarea zarului - funcţia roll() şi graficul aferent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q7. Valoarea aşteptată este o proprietate a:\n",
    "\n",
    "1. statisticii\n",
    "2. variabilităţii\n",
    "3. distribuţiei\n",
    "4. matematicii"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def q():\n",
    "    return 3\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(7, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q8. Media populaţiei este centrul de masă al:\n",
    "\n",
    "1. distribuţiei\n",
    "2. populaţiei\n",
    "3. sample-ului\n",
    "4. familiei"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def q():\n",
    "    return 2\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(8, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q9. Sample mean este centrul de masă al:\n",
    "\n",
    "1. datelor observate\n",
    "2. familiei\n",
    "3. populaţiei\n",
    "4. distribuţiei"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def q():\n",
    "    return 1\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(9, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q10. Media populaţiei estimează sample mean? (da/nu) \n",
    "Este sample mean unbiased? (da/nu) \n",
    "Pe măsură ce adăugăm mai multe experimente sample-ului, devine densitatea de probabilitate din ce în ce mai concentrată în jurul mediei populaţiei? (da/nu)\n",
    "\n",
    "Daţi un răspuns de genul 'x/x/x', unde x este 'da' sau 'nu'."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def q():\n",
    "    return 'nu/da/da'\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(10, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Variabilitate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Variance (dispersia) pentru o variabilă aleatoare măsoară împrăştierea acesteia faţă de medie. Ea, ca şi media, este determinată ca valoarea aşteptată a pătratului diferenţei faţă de medie:\n",
    "\\begin{equation}\n",
    "Var(X) = E( (X - \\mu)^2 ) = E( (X - E(X))^2 ) = E(X^2) - E(X)^2\n",
    "\\end{equation}\n",
    "\n",
    "Vom considera proprietatea de liniaritate a dispersiei, $Var(aX) = a^2 Var(X)$:\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{split}\n",
    "Var(aX) &= E((aX)^2) - E(aX)^2 \\\\\n",
    "&= E(a^2X^2) - (aE(X))^2 \\\\\n",
    "&= a^2E(X^2) - a^2E(X)^2 \\\\\n",
    "&= a^2Var(X)\n",
    "\\end{split}\n",
    "\\end{equation}\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q11. Fie o populaţie a aruncărilor cu zarul. Probabilitatea fiecărei feţe este $1/6$. Care este valoarea aşteptată a feţei care va ieşi (media)? Încercaţi să nu introduceţi valoarea direct ci să scrieţi cod numpy care o calculează."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evenimente posibile: [1 2 3 4 5 6]\n",
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "x = np.array(range(1, 7))\n",
    "print('Evenimente posibile:', x)\n",
    "\n",
    "def q():\n",
    "    return np.sum(x*1/6)\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(11, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q12. Mai departe, care este valoarea aşteptată a pătratului variabilei aleatoare x de mai sus?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evenimente posibile: [1 2 3 4 5 6]\n",
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "x = np.array(range(1, 7))\n",
    "print('Evenimente posibile:', x)\n",
    "\n",
    "def q():\n",
    "    r=[X**2 for X in x]\n",
    "    return np.sum(r)/6\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(12, np.round(q(), 3)) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q13. În continuare, care este valoarea dispersiei? Calculaţi-o ca diferenţa dintre valoarea aşteptată a pătratelor variabilei aleatoare X şi pătratul mediei sale:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Evenimente posibile: [1 2 3 4 5 6]\n",
      "2.917\n",
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "x = np.array(range(1, 7))\n",
    "print('Evenimente posibile:', x)\n",
    "\n",
    "def q():\n",
    "    r=[X**2 for X in x]\n",
    "    media1=np.sum(r)/6\n",
    "    media2=np.sum(x)/6\n",
    "    return media1-media2**2\n",
    "print(np.round(q(), 3))\n",
    "print('Raspuns %s' % ('corect' if r(13, np.round(q(), 3)) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q14. Considerăm dispersia mediei sample-urilor pentru o variabilă aleatoare, adică $Var(\\bar{X})$. Presupunem $n$ variabile independente $X_i$. Care din următoarele este expresia lui $Var(\\bar{X})$?\n",
    "\n",
    "1. $Var(1/n * \\sum_i X_i)$\n",
    "2. $E(1/n * \\sum_i X_i)$\n",
    "3. $\\sigma$\n",
    "4. $\\mu$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def q():\n",
    "    return 1\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(14, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q15. Cu care din următoarele este egală $Var(1/n * \\sum_i X_i)$ ? Folosiţi proprietatea de liniaritate a dispersiei.\n",
    "\n",
    "1. $1/n^2 * E(\\sum_i X_i)$\n",
    "2. $\\mu / n^2$\n",
    "3. $1/n^2 * Var(\\sum_i X_i)$\n",
    "4. $\\sigma / n$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def q():\n",
    "    return 3\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(15, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q16. Mai departe, cu ce este egală $Var(\\sum_i X_i)$? Atenţie, variabilele aleatoare $X_i$ sunt independente.\n",
    "\n",
    "1. $\\sum_i Var(X_i)$\n",
    "2. $E(\\sum_i X_i)$\n",
    "3. $Var(\\sigma)$\n",
    "4. $E(\\mu)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def q():\n",
    "    return 1\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(16, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q17. Mai departe, fiecare $X_i$ provine dintr-o populaţie cu dispersie $\\sigma^2$. Cu ce este egală $\\sum_i Var(X_i)$ ?\n",
    "\n",
    "1. $n^2 * Var(\\sigma)$\n",
    "2. $n * E(\\mu)$\n",
    "3. $n * \\mu$\n",
    "4. $n * \\sigma^2$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "def q():\n",
    "    return 4\n",
    "\n",
    "print('Raspuns %s' % ('corect' if r(17, q()) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q18. În cele ce urmează ne propunem să verificăm modul de calcul teoretic al standard error. Ne reamintim cum funcţionează aceasta pentru evenimentele reprezentînd aruncarea monezii:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.15811388300841897\n",
      "0.16038662163659412\n",
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "# Pentru o moneda cu probabilitatea p sa iasa Head, avem:\n",
    "# * media este p\n",
    "# * dispersia (variance) este p*(1-p), sau p*p daca moneda este ideala\n",
    "#   in acest ultim caz, deviatia standard este tot p\n",
    "\n",
    "# generam o matrice de 10000 x 10 de aruncari fair, valori intre 0 si 1\n",
    "nosim, n = 10000, 10\n",
    "x = np.random.randint(low=0, high=2, size=(nosim, n))\n",
    "\n",
    "# fiecare sample consta din 10 aruncari; calculam media acestor 10 aruncari\n",
    "x = np.mean(x, axis=1)\n",
    "\n",
    "# calculam deviaţia standard a mediei (radical din standard error) teoretic\n",
    "print(0.5/np.sqrt(n))\n",
    "\n",
    "# calculam deviaţia standard folosind numpy\n",
    "print(np.std(x))\n",
    "\n",
    "# calculati deviatia standard de mana, pornind de la sample-ul x, scriind explicit formula:\n",
    "def stddev(x):\n",
    "    r=[X**2 for X in x]\n",
    "    media1=np.sum(r)/len(r)\n",
    "    media2=np.sum(x)/len(x)\n",
    "    variance=media1-media2**2\n",
    "    return np.sqrt(variance)\n",
    "#print(np.round(stddev(x),16))\n",
    "\n",
    "print('Raspuns %s' % ('corect' if np.round(stddev(x),14) == np.round(np.std(x),14) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "__Notă__: cam 1/10 din cazuri o să primiţi 'răspuns incorect', chiar dacă rezolvarea e bună.\n",
    "\n",
    "Q19. Realizaţi acelaşi calcul, de data aceasta pentru evenimentele aruncării cu zarul:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.5 2.9166666666666665\n",
      "0.15840535849522264\n",
      "0.15811388300841897\n",
      "Raspuns corect\n"
     ]
    }
   ],
   "source": [
    "x = np.array([1, 2, 3, 4, 5, 6])\n",
    "mu = np.mean(x)\n",
    "sigma = np.var(x)\n",
    "print(mu, sigma)\n",
    "\n",
    "nosim, n = 10000, 10\n",
    "x = np.random.randint(low=0, high=2, size=(nosim, n))\n",
    "x = np.mean(x, axis=1)\n",
    "\n",
    "# calculati standard error of the mean\n",
    "def stderror(sigma, n):\n",
    "    return 0.5/np.sqrt(n) #sigma/np.sqrt(n)\n",
    "\n",
    "print(np.std(x))\n",
    "print(stderror(sigma, n))\n",
    "\n",
    "print('Raspuns %s' % ('corect' if np.round(stderror(x, n), 2) == np.round(np.std(x), 2) else 'incorect'))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Q20. a) Pentru o distribuţie normală de medie 10 şi dispersie 2, consideraţi un număr variabil de sample size-uri pe care le extrageţi din distribuţie: 10, 20, 40, 60 de sample-uri. Calculaţi media pe sample. Repetaţie de \n",
    "10000 de ori. Ridicaţi histogramele distribuţiei mediei sample-ului (sample mean).\n",
    "\n",
    "b) Realizaţi acelaşi lucru şi pentru distribuţia dispersiei (variance).\n",
    "\n",
    "Observaţi valorile unde se centrează distribuţiile obţinute."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0.98, 'Distribuţia dispersiei sample-ului(variance)')"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x360 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu, sigma = 10,2 # mean and standard deviation\n",
    "def distributieNormala(mu, sigma, no_samples):\n",
    "    s = [np.random.normal(mu, sigma, no_samples).mean() for x in range(10000)]\n",
    "    return s\n",
    "    #s = np.random.normal(mu, sigma, (10000,no_samples))\n",
    "    #return np.average(s, axis=1)\n",
    "\n",
    "\n",
    "fig, (ax1, ax2, ax3, ax4) = plt.subplots(1, 4, sharey=True, figsize=(15, 5))\n",
    "kwargs = dict(rwidth=0.7, density=True, alpha=0.75, ec='k', linewidth=2)\n",
    "\n",
    "n, bins, patches=ax1.hist(distributieNormala(mu, sigma,10), 30,**kwargs, facecolor='pink')\n",
    "\n",
    "n, bins, patches=ax2.hist(distributieNormala(mu, sigma,20), 30, **kwargs,facecolor='red')\n",
    "\n",
    "n, bins, patches=ax3.hist(distributieNormala(mu, sigma,40), 30, **kwargs,facecolor='blue')\n",
    "\n",
    "n, bins, patches=ax4.hist(distributieNormala(mu, sigma,60), 30, **kwargs,facecolor='green')\n",
    "fig.suptitle('Distribuţia mediei sample-ului(sample mean)', fontsize=16)\n",
    "\n",
    "def distributieDispersiei(mu, sigma, no_samples):\n",
    "    s = np.random.normal(mu, sigma, (10000,no_samples))\n",
    "    return np.var(s, axis=1,ddof=1)\n",
    "\n",
    "fig, (ax1, ax2, ax3, ax4) = plt.subplots(1, 4, sharey=True, figsize=(15, 5))\n",
    "kwargs = dict(rwidth=0.7, density=True, alpha=0.75, ec='k', linewidth=2)\n",
    "\n",
    "n, bins, patches=ax1.hist(distributieDispersiei(mu, sigma,10), 30,**kwargs, facecolor='pink')\n",
    "\n",
    "n, bins, patches=ax2.hist(distributieDispersiei(mu, sigma,20), 30, **kwargs,facecolor='red')\n",
    "\n",
    "n, bins, patches=ax3.hist(distributieDispersiei(mu, sigma,40), 30, **kwargs,facecolor='blue')\n",
    "\n",
    "n, bins, patches=ax4.hist(distributieDispersiei(mu, sigma,60), 30, **kwargs,facecolor='green')\n",
    "fig.suptitle('Distribuţia dispersiei sample-ului(variance)', fontsize=16)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
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