mar13p - EXAM P QUESTIONS OF THE WEEK S. Broverman, 2006...

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EXAM P QUESTIONS OF THE WEEK S. Broverman, 2006 Week of March 13/06 The random variable has density function for . \ 0ÐBÑœ-/ ∞B∞ lBl Find the variance of . \ The solution can be found below.
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Week of March 13/06 - Solution In order for to be a properly defined density function, it must satisfy . 0ÐBÑ 0ÐBÑ.B œ " ' ∞ The integral is '' ' ' ∞ ∞ ∞ ! ∞∞ ! lBl B B 0ÐBÑ.B œ -/ .B œ - † Ò / .B  / .BÓ œ - † Ò"  "Ó œ " , from which it follows that . " # Then, . Z+<Ò\ÓœIÒ\ ÓÐIÒ\ÓÑ ## IÒ\Ó œ B/ .B œ † Ò B/ .B  B/ .BÓ ' ∞ ∞ ! ∞! "" lBl B B . We use the integration by parts rule . ' B/ .B œ +B B/ / ++ +B +B # Then , ' ¹ ∞ ! BB B Bœ∞ Bœ! B/ .BœB/ /
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This note was uploaded on 03/29/2010 for the course STATISTICS 50 taught by Professor Diaz during the Spring '10 term at California State University , Monterey Bay.

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mar13p - EXAM P QUESTIONS OF THE WEEK S. Broverman, 2006...

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