Let X and Y be random variables. The covariance Cov(X, Y) is defined by(see Exercise 6.2.23) cov(X, Y) = E((X – 4(X))(Y – µ(Y))) .- (a) Show that cov(X, Y)

= E(XY) – E(X)E(Y).%3D (b) Using (a), show that cov(X,Y) = 0, if X and Y are independent. (Caution: the converse is not always true.) (c) Show that V(X +Y) V(X)+V(Y)+2cov(X,Y).