Bivariate continuous trinomial distribution $f(x,y)=C \times λ_{1}^x \times λ_{2}^y \times (1-λ_{1}-λ_{2})^{1-x-y}$
where $0 < x < 1, 0 < y < 1, 0 < x + y < 1$ .
This distribution has two parameters, $λ_{1}, λ_{2}$ , and the parameter space are
$0<λ_{1}<1, 0<λ_{2}<1$ .
Let $f(x)=\int f(x,y)dy$ . and $X$ is not Continuous Bernoulli distribution( $λ_{1}$ ).
Let $f(y)=\int f(x,y)dx$ , and $Y$ is not Continuous Bernoulli distribution( $λ_{2}$ ).
The marginal probability density function of $X$ and $Y$ have two parameters, $λ_{1}, λ_{2}$ and $\int f(x)dx= \int f(y)dy=1$ .
$X$ and $Y$ are not independent random variables.
$X+Y$ is not Continuous Bernoulli distribution ( $λ_{1}, λ_{2}$ ).
The $(x,y,f(x,y))$ dynamic diagrams is affected by $λ_{1}$ and setting $λ_{1}+λ_{2}=c$ .
This displayed method can understand $f(x,y)$ diagram changed when the $λ_{1}$ different value in simply.
1. $X$ ~ Continuous Bernoulli distribution ( $λ$ ) $f(x) = C \times λ^{x} \times (1 - λ)^{1 - x}$ , $0 < x < 1$ ,
$\int f(x)dx = 1$ .
Let $λ =0.01$ to $0.99$ and step $= 0.01$ .
Video
2. $(x,y,f(x,y))$ dynamic diagrams $λ_{1} + λ_{2} = 0.1$ , $λ_{1} = 0.01$ to $0.099$ and step $= 0.001$
Video for case 1
Video for case 1 of X
Video for case 1 of Y
