X and Z are two jointly distributed random variables. Suppose you know the value of Z, but not the value of . Let X = E( X| Z) denote a guess of the value of X using the information on Z, and let W =  denote the error associated with this guess.
(a) Show that E(W) = 0.
(b) Show that E(WZ) = 0.
(c) Let = g(Z) denote another guess of X using Z, and V = X -  denote its error. Show that E(V2) E(W2).