Problem 6 Let X and Y be two random variables and let a, b, c, and d be real numbers. The covariance of X and Y is defined as Cov(X, Y) = E[(X - E[X])(Y - ELY])]. Show that Cov(X, Y) = E[XY] - E[X]ELY]. Show that Cov(aX + c, by + d) = Cov(ax, by). Show that Var (X + Y) = Var(X) + Var(Y) + 2Cou(X, Y)