Let X and Y be two continuous random variables with joint density (PDF) fxy(x, y). (a) Show that if X and Y are independent, they are also uncorrelated. (b) Now let the joint PDF of X and Y be given by fxy (x, y) = {A(x + y), 1 x1, 0 y1 = otherwise and find the constant A and determine if X and Y are independent. (c) Now let X = cos and Y = cos p, where is a uniform random variable in the interval (0,). Show that X and Y are uncorrelated but not independent.