(a) Let c be a constant and X a random variable with expected value E(X) and variance Var(X). Show that E[(X - c)2] = Var(X) + (c- (E(X))). = (b) Suppose that X and Y are random variables with expected values E(X) E(Y) = 0, variances Var(X) and Var(Y), and covariance Cov(X, Y). Show that Var(XY) Var(X)Var(Y) = Cov(X, Y2) - [Cov(X, Y)]. (c) It can be shown that if two random variables are independent then E(g(x)h(Y)) = E(g(X))E(h(Y)). Show that the Cov(X, Y) = 0 if X and Y are two independent random variables.