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Let X and Y have joint probability mass function f X , Y ( x , y ) : = p 2 ( 1 p

Let X and Y have joint probability mass functionfX,Y(x,y):=p2(1p)y2 if x<yfor positive integers x and y and p(0,1).

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

b) Find the conditional probability mass function of Y given that X = x, a positive integer.

c) Find the conditional probability mass function ofZ=YX given that X = x, a positive integer.

d) Are Z and X independent?

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