Let X, Y, and Z = E[X|Y] be as in Problem 13. Define the random variable V as V = Var(X|Y).

a. Find the PMF of V.

b. Find EV.

c. Check that V ar(X) = EV +V ar(Z).

Problem 13

Consider two random variables X and Y with joint PMF given in Table 5.5

Define the random variable Z as Z = E[X|Y].

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Table 5.5: Joint PMF of X and Y in Problem 13 X=0 X = 1 Y = 0 6 1 Y = 1 1 Y = 2