Practice quiz6 and soln

# Practice quiz6 and soln - Practice questions for Quiz 6 to...

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Practice questions for Quiz 6 to be given on October 27 ______1. Suppose that X has mean μ =5 and σ =10 and Y= 6- 4X. The standard deviation of Y equals_____ _____2. Suppose that X 1 , X 2 and X 3 have mean μ =5 and σ 2 = 4 and Cov(X j , X k ) =0 for j k . Then the variance of Y= X 1 – X 2 + 2X 3 equals_______ 3-4. Suppose we take a random sample of n=4 values of X. We let X 1 denote the first value in the sample, X 2 denote the second value, X 3 denote the 3 rd value and X 4 denote the 4 th value. Given (1) μ 1 = μ 2 = μ 3 = μ 4 = μ x = 2 and (2) σ 1 = σ 2 = σ 3 = σ 4 2 x =9. Let 4 4 1 = = i i X X . _______ 3. Regardless of the value of N, the mean value of X equals____ ________ 4. If N>> 4 then Cov(X j , X k ) = 0 for all j ≠k and the X j are independent, so Var( X ) = ____ 1

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SOLUTIONS TO QUIZ 4A ___ 40 ___ 1. Suppose that X has mean μ =5 and σ =10 and Y= 6- 4X. The standard deviation of Y equals_____ Y= 6-4X. If Y=aX + b then  σ 2 Y  = a 2 σ 2 x   and  σ =|a| σ Y Here a=-4,  so |a| =4,  and  σ x  =10. So  σ Y =|a| σ x =|-4|x10   = 40 . 24     ___     2. Suppose that X 1 , X 2 and X 3 have mean μ =5 and σ 2 = 4 and Cov(X j ,X k )=0 for j k . Then the variance
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• Fall '03
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