(a) [14 POINTS Let X and Y be two random variables with E (X) = Hx, V (X) = ox, E(Y) = My V (Y) = of and COV (X, Y) = oxy. Assume that X and Y are independent. Show that V( Y - X) - of tox. (b) [15 POINTS] Let X and Y be two discrete random variables with joint probability distribution y -1 1 5 -2 0.4 0 0.2 1 0.1 0.3 0 I (i) It is known that E (X) = -0.8 and E (Y) = 0.8. Compute COV (X, Y). (ii) The marginal distributions g (x) and h (y) are -2 1 y -1 1 5 g (x) 0.6 0.4 ' h (y) 0.5 0.3 0.2 Calculate the conditional probability distribution w (y | - 2)