Let X and Y be r.v.s defined on the probability space ((, A, P), and suppose that
Question:
(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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i We have Var XY X XY 2 Y by definition X 2 XY 2 2X XY Y X 2 Y ...View the full answer
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Related Book For 
An Introduction to Measure Theoretic Probability
ISBN: 978-0128000427
2nd edition
Authors: George G. Roussas
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