Question 4 Miscellaneous (a) Consider two random variables X, Y which have the property that E(XY) = E(X)E(Y). Show that V(X+Y) = V(X)+V(Y). (Note: it is true that E (g, (X) + 92(Y)) = E(g1 (X))+ E(gz (Y)). (b) Let W ~ Cauchy(0, 1) be a Cauchy-distributed random variable, which has density fw(w) = {n (1+w?) } , -00