The covariance of two real-valued random variables X and Y with expectations X = E[X]

and _Y = E[Y] is the quantity

Cov(X; Y ) = E[(X - _X)(Y - _Y)].

(a) Show that Cov(X, Y) = E[XY] - _XY.

(b) Show that Cov(X, Y) = 0 whenever X and Y are independent.