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problemset31 - STAT/MA 416 November 9, 2011 Problem Set 31...

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STAT/MA 416 November 9, 2011 Problem Set 31 Name: 1a. If X 1 ,X 2 ,X 3 ,X 4 ,X 5 are independent random variables that each have average 8.2 and variance 32.49, then the sum of the X j ’s is normal. Thus, if we divide the sum of the X j ’s by 5, we get the average of the X j ’s, which is normal too: Y = X 1 + X 2 + X 3 + X 4 + X 5 5 . Find the expected value E ( Y ), and ﬁnd the variance Var( Y ). 1b. If X 1 ,X 2 ,...,X n are independent random variables that each have average μ and variance σ 2 , then the sum of the X j ’s is normal. Thus, if we divide the sum of the X j ’s by n , we get the average of the X j ’s, which is normal too: Y = X 1 + X 2 + ··· + X n n . Find the expected value E ( Y ), and ﬁnd the variance Var( Y ). 1

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Assume that the quantity of money in a randomly-selected checking account is normal with mean \$1325 and standard deviation \$25. Also assume that the amounts in diﬀerent accounts of diﬀerent people are independent. Let X be the sum of the money contained
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This note was uploaded on 02/28/2012 for the course STAT 416 taught by Professor Staff during the Fall '08 term at Purdue University-West Lafayette.

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problemset31 - STAT/MA 416 November 9, 2011 Problem Set 31...

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