Quiz6 with soln

# Quiz6 with soln - Quiz 6 October 27 Print your name here...

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Quiz 6 October 27 Print your name here: ___________________________ ID #__________ (use all UPPER CASE letters) ______1. Suppose that X has mean μ =2 and σ =1 and Y= 3- 2X. The standard deviation of Y equals_____ _____2. Suppose that X 1 and X 2 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 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 = 8 and (2) σ 1 = σ 2 = σ 3 = σ 4 2 x =10. Let 4 4 1 = = i i X X . Because each of the Xj are random variables, X is a random variable. _______ 3. The mean value of X equals____ ________ 4. If the population size, 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 6 ___ 2 ___ 1. Suppose that X has mean μ =1 and σ =1 and Y= 3- 2X. The standard deviation of Y equals_____ Y= 3-2X. If Y=aX + b then  σ 2 Y  = a 2 σ 2 x   and  σ =|a| σ X Here a=-2,  so |a| =2,  and  σ x  =1. So
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