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solutiontomid1 - Solutions to Midterm Exam 1 Hongyan Zhao...

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Solutions to Midterm Exam 1 * Hongyan Zhao Oct 5, 2009 Q1 a. (5 points) A b. (5 points) A c. (5 points) C+D d. (5 points) B+A/2 or 1-(C+D) Q2 a. (7 points) E ( ¯ X dodd ) = E ( 1 n n/ 2 X i =1 2 x 2 i - 1 ) = 1 n n/ 2 X i =1 2 E ( x 2 i - 1 ) = 1 n · n 2 · 2 μ = μ So, the double odds estimator is unbiased. b. (8 points) V ar x dodd ) = V ar ( 1 n n/ 2 X i =1 2 x 2 i - 1 ) = 1 n 2 n/ 2 X i =1 V ar (2 x 2 i - 1 ) = 1 n 2 · n 2 · 4 σ 2 = 2 n σ 2 V ar x odd ) = V ar ( 2 n n/ 2 X i =1 x 2 i - 1 ) = 4 n 2 n/ 2 X i =1 V ar ( x 2 i - 1 ) = 1 n 2 · n 2 · σ 2 = 2 n σ 2 V ar x dodd ) = V ar x odd ) So, the double odds estimator is not more efficient than the odds estimator. Q3 a. (6 points) 36 52 b. (6 points) 35 51 c. (6 points) P ( X = 1) = 1 - P ( X = 0) = 1 - 36 52 · 35 51 0 . 5249 d. (6 points) P ( Y = 1) = 1 - P ( Y = 0) = 1 - 48 52 · 47 51 0 . 1493 * If you find any mistake or typo, please email me [email protected] 1
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e. (6 points) P ( X = 1 ,Y = 1) = C 1 4 C
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solutiontomid1 - Solutions to Midterm Exam 1 Hongyan Zhao...

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