1. The random variables X, Y have joint p.m.f. 0.1 if x = 1,y =4, 0.3 if x = 1, y = 5, 0.1 if x = 4, y = 4, fx, y (I, y) 4 5 fx,y (I, y) = 0.1 0.3 0.1 if x = 4, y =5, i.e., 0.1 0.1 0.2 if x = 5, y = 4, 5 0.2 0.2 0.2 if x = 5, y = 5, otherwise, (a) Compute P(X 2 Y). [2 marks] (b) Compute E(XY). [2 marks] (c) Find the marginal p.m.f.'s fx(x) and fr(y). [3 marks] (d) Compute E(X) and E(Y). [2 marks] (e) Compute E(2X + Y). [2 marks] (f) Are X and Y independent? Explain your answer. [1 marks] (g) Find the conditional p.m.f. fxA(x) for A = {X > Y}. [2 marks] (h) Find E (X | A) for A = {X 2 Y}. [2 marks] (i) Find the conditional p.m.f. frix(ylx) for Y given X. [3 marks] (j) Find E (Y [ X). [2 marks] (k) Compute Cov(X, Y). [2 marks] (1) Compute px,Y . [5 marks]