Let the conditional p.d.f. of X given Y be g1(x|y) = 3x2/y3 for 0 < x < y and 0 otherwise. Let the marginal p.d.f. of Y be f2(y), where f2(y) = 0 for y ≤ 0 but is otherwise unspecified. Let Z = X/Y. Prove that Z and Y are independent and find the marginal p.d.f. of Z.