Question: Let X and Y be r.v.s defined on the probability space ((, A, P), and suppose that X2 < (. Then show that (i) The

Let X and Y be r.v.s defined on the probability space ((, A, P), and suppose that εX2 < (. Then show that
(i) The conditional variance of X, given Y, is given by the formula
Var (X | Y) = ε{[X - ε(X | Y)]2 |Y}
= ε(X2 | Y) - [ε(X | Y)]2 a.s.
(ii) Var(x) = ε[Var (X | Y)] + Var [ε(X | Y)].

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