20. The Conditional Covariance Formula. The conditional covariance of X and Y, given Z, is defined by Cov(X, Y|Z) = E[(X − E[X|Z])(Y − E[Y|Z])|Z]

(a) Show that Cov(X, Y|Z) = E[XYZ] − E[X|Z]E[Y|Z]

(b) Prove the conditional covariance formula Cov(X, Y) = E[Cov(X, Y|Z)] + Cov(E[X|Z], E[Y|Z]).

(c) Set X = Y in part

(b) and obtain the conditional variance formula.