(Independence) Suppose that X and Y are independent. Prove that for any A C R and B C R, we have P(X E A,Y E B): P(X E A)P(Y E B). You may make use of the following hints: (i) We learned that if X and Y are independent, then for any functions 9 and h, E(g(X)h(Y>> = E(y(X)) Ema. (ii) Let I denote the indicator function. For any A C R, we have E(I(X EA)) :1 X P(X EA)-|0>