Question: X and Z are two jointly distributed random variables. Suppose you know the value of Z, but not the value of . Let X =

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).

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