Two discrete random variables X , Y have the joint probability density function

where X, p are constants with X > 0 and 0

(a) Find the marginal probability density functions of X and Y.

(b) Find the conditional probability density function of X given Y.

Px.x(x,y) e-p(1 - p) y! (x - y)! 0 if y 0, 1,...,x,x=0,1,2,... = otherwise,