Prove Theorem 4.7.4. In Theorem 4.7.4. Law of Total Probability for Variances. If X and Y are

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Prove Theorem 4.7.4.
In Theorem 4.7.4.
Law of Total Probability for Variances. If X and Y are arbitrary random variables for which the necessary expectations and variances exist, then Var(Y) = E[Var(Y |X)] + Var[E(Y|X)].

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Probability And Statistics

ISBN: 9780321500465

4th Edition

Authors: Morris H. DeGroot, Mark J. Schervish

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Question Posted: Nov 25, 2015 03:34 AM

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Prove Theorem 4.7.4. In Theorem 4.7.4. Law of Total Probability for Variances. If X and Y are

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Let EY Y Then Var Y EY Y 2 EY EY X EY X Y 2 EY EY X 2 2EY EY XEY X Y EEY X Y 2 We shall now c...View the full answer

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