2. Let X and Y be two random variables. Suppose XY ~ Binomial (n, Y) where n is fixed and Y stands for the probability of success. Suppose the success probability Y is a random variable distributed as a Beta distribution, Y Beta(a, B). The PDF of Beta(a, B) is defined by the following { 0 < y < 1,a > 0, B>0, f(y) = 0, otherwise, where B(a, B) r(a)I(5) T(a+B)* (1) Find E(X|Y) and V(X|Y). (2) Find E(X). (3) Find Cor(X,Y). Hint: E(X|Y) is a linear function of Y. (4) Find the conditional PDF of Y given X = r. 3. Suppose X and Y

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