Two discrete random variables X and Y have the joint probability density function: f(x,y)='e"p" (1-p)*Y y!(x-y)! x-y y 0,1,2,..,x; x-0,1,2,... where 1, p are constants with 2 >0 and 0

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Two discrete random variables X and Y have the joint probability density function:
f(x.y)=e*p" (1-p)*
y!(x-y)!
x-y
,y 0,1,2,..,x; x 0,1,2,...
where 2, p are constants with 2 >0 and 0 <p<1.
1. Find the marginal probability density functions of X and Y.
2. Find the conditional distribution of Y for a given X and of X for a given Y.
Transcribed Image Text:Two discrete random variables X and Y have the joint probability density function: f(x.y)=e*p" (1-p)* y!(x-y)! x-y ,y 0,1,2,..,x; x 0,1,2,... where 2, p are constants with 2 >0 and 0 <p<1. 1. Find the marginal probability density functions of X and Y. 2. Find the conditional distribution of Y for a given X and of X for a given Y.
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