For any three random variables X, Y, and Z with finite variances, prove (in the sprit of Theorem 4.4.7) the covariance identity
Cov(X, Y) = E(Cov(X, Y|Z)) + Cov(E(X|Z),E(Y|Z)),
where Cov(X, Y|Z) is the covariance of X and Y under the pdf f(x, y|z).