This exercise provides an example ofa pair of random variables X and Y for which the conditional mean of Y given X depends on X but corr(X.Y) = 0. Let X and Z be two independently distributed standard normal random variables, and let Y = X2 + Z. Show that E(Y|X) = X2. Show that = 1. Show that E(XY) = 0. (Hint: Use the fact that the odd moments of a standard normal random variable are all zero.) Show that cov(X.Y) = D and thus corr(X,Y) = 0