1. (Total 8 points) Consider a discrete pair of random variables (X, Y ) with joint PMF f x x (x, y) = 16 (x + y) for x = 0, 1 and y = 0, 1, 2, 3 = 0 otherwise. (a) (1 point ) What is the marginal PMF of Y, fy(y)? (b) (1 point) What are E(Y) and Var(Y)? (c) (1 point) What are E(XY) and Var(XY)? (d) (1 point) What is Cov(X, Y)? (e) (1 point) What is the conditional PMF of X given Y, i.e., fxy (xly)? (f) (1 point) What is the conditional CDF of X given Y, i.e., Fxy(xly)? (g) (1 point) What are the conditional expectation and conditional variance of X given Y = 3, i.e., E(X|Y = 3) and Var(X|Y = 3)? (h) (1 point ) Derive the CDF of X2Y