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metricsexam0f08sol

metricsexam0f08sol - Econometrics Exam 0 Sept 5 2008 By...

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Econometrics Exam 0 By writing your PID below, you are indicating Sept. 5, 2008 your intention to abide by the honor pledge: PID: This exam consists of ten short questions ( worth four points apiece ) and three long questions ( worth twelve points each ) , for a total of 76 points. You have 50 minutes to answer all completely and clearly in the space provided. For better and for worse, I am grading you primarily on technique and secondarily on correct answers. Short Questions 1. Suppose that X has a mean of 5 , and variance of 9 ; Y has a mean of 7 , and variance of 16 ; the two random variables are independent. If you created Z = 2 X ! Y , what would be E [ Z ] and Var ( Z ) ? E [ Z ] = E [2 X ! Y ] = E [2 X ] ! E [ Y ] = 2 E [ X ] ! E [ Y ] = 2 " 5 ! 7 Var ( Z ) = Var (2 X ! Y ) = Var (2 X ) + Var ( ! Y ) + 2 Cov (2 X , ! Y ) = (2) 2 Var ( X ) + ( ! 1) 2 Var ( Y ) + 2(2)( ! 1) Cov ( X , Y ) = 4 " 9 + 1 " 16 ! 4 " 0 2. Given three matrices A , B , and C , rewrite the expression ( A + BC ! ) without parentheses. ( A + BC ! ) = ( A ! ) + ( BC ! ) = ! A + ! C ! B 3. What is the difference between “ Var ( X ) ” and “ V ˆ ar ( X ) ”? Var ( X ) ” refers to the true variance in X in the population; “ V ˆ ar ( X ) is the variance that the researcher calculates for his sample of the population.

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