Question: 19. Let X and Y be continuous random variables. Prove that E 4!X E(X|Y )25 = E(X2 ) E 4 E(X|Y )25 .

19. Let X and Y be continuous random variables. Prove that E 4!X − E(X|Y )"25 = E(X2 ) − E 4 E(X|Y )25 . Hint: Let Z = E(X|Y ). By conditioning on Y and using Example 10.23, first show that E(XZ) = E(Z2).

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