22. Suppose that X and Y are jointly distributed as indicated in the table. X PxY (x, y) 0 2 4 8 0 0.02 0.04 0.01 0.03 1 0.04 0.08 0.02 0.06 2 0.06 0.12 0.03 0.09 3 0.08 0.16 0.06 0.10 a. Find P[X = 2Y] b. Find the joint c.d.f. of X and Y, Fxy (x, y) Find E [XY] d. Find the marginal p.m.f.'s of X and Y: Px(x) and py (y) e. Find the conditional p.m.f. of X given Y=2: Pxy=2(x) f. Find E [X|Y = 2] and Var [X|Y = 2] Are X and Y independent? h. Find the covariance and the correlation coefficient of X and Y: Cov(X, Y ) and Pxy