Let X, Y, and Z = E[X|Y] be as in Example 5.11. Let also V =Var(X|Y). a.

Question:

Let X, Y, and Z = E[X|Y] be as in Example 5.11. Let also V =Var(X|Y).

a. Find the PMF of V .

b. Find EV.

c. Check that Var(X) = E(V )+Var(Z).


Example 5.11:

Consider two random variables X and Y with joint PMF given in Table 5.2. Let Z = E[X|Y].

X = 0 X=1 Y = 0 16 25 Y=1 235 0

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