From 0f73eca7ae4a959d55812d3737232380337b9894 Mon Sep 17 00:00:00 2001 From: Nahin Khan Date: Mon, 7 Feb 2022 21:07:32 +0300 Subject: [PATCH] Correct PMF domain and codomain (#211) --- preliminaries/probabilityreview/index.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/preliminaries/probabilityreview/index.md b/preliminaries/probabilityreview/index.md index cff3b96..8dbfce7 100644 --- a/preliminaries/probabilityreview/index.md +++ b/preliminaries/probabilityreview/index.md @@ -103,7 +103,7 @@ By using this function, one can calculate the probability that $$X$$ takes on a ## 2.2 Probability mass functions -When a random variable $$X$$ takes on a finite set of possible values (i.e., $$X$$ is a discrete random variable), a simpler way to represent the probability measure associated with a random variable is to directly specify the probability of each value that the random variable can assume. In particular, a probability mass function (PMF) is a function $$p_X : \Omega \to \Re$$ such that $$p_X(x) = P(X = x)$$. +When a random variable $$X$$ takes on a finite set of possible values (i.e., $$X$$ is a discrete random variable), a simpler way to represent the probability measure associated with a random variable is to directly specify the probability of each value that the random variable can assume. In particular, a probability mass function (PMF) is a function $$p_X : \Re \to [0, 1]$$ such that $$p_X(x) = P(X = x)$$. In the case of discrete random variable, we use the notation $$Val(X)$$ for the set of possible values that the random variable $$X$$ may assume. For example, if $$X(\omega)$$ is a random variable indicating the number of heads out of ten tosses of coin, then $$Val(X) = \{0, 1, 2, \dotsc, 10\}$$.