If X and Y are any two random variables, then the covariance of X and Y is defined by Cov(X, Y) = E ((X −E(X))(Y −E(Y ))). Note that Cov(X, X) = V (X). Show that, if X and Y are independent, then Cov(X, Y) = 0; and show, by an example, that we can have Cov(X, Y) = 0 and X and Y not independent.