Question: 25. Let X and Y be continuous random variables. Prove that Hint: Let Z = E(X|Y ). By conditioning on Y and using Example 10.21,

25. Let X and Y be continuous random variables. Prove that

E[(X E(X|Y))] = E(X) E[E(X\Y)].

Hint: Let Z = E(X|Y ). By conditioning on Y and using Example 10.21, first show that E(XZ) = E(Z2).

E[(X E(X|Y))] = E(X) E[E(X\Y)].

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