B4090.HW2

# B4090.HW2 - BTRY 4090 STSCI 4090 Spring 2011 Homework 2 Due...

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BTRY 4090 / STSCI 4090 Spring 2011 Homework 2 Due at 2:00pm on Friday, February 11 in 1198 Comstock Hall Read Homework Policy and Instructions before you begin this assignment. Use computer software of your choice for calculations too laborious to be feasible manually. 1. Larsen & Marx p. 297, Question 5.2.16. 2. Larsen & Marx p. 297, (a) Question 5.2.20. In addition, (b) Find the maximum likelihood estimates for θ 1 and θ 2 . 3. Larsen & Marx p. 309, Question 5.3.2. 4. Larsen & Marx p. 311, Question 5.3.22. Note: In (a), make the simple (but incorrect) assumption that the number of successes is binomial; in (b), assume it is hypergeometric. 5. Larsen & Marx p. 311, Question 5.3.28. 6. Larsen & Marx p. 316, Question 5.4.2. 7. Larsen & Marx p. 316, Question 5.4.6. 8. Larsen & Marx p. 317, Question 5.4.14. As stated in L&M: (a) Is 1 min ˆ nY unbiased for θ ? (b) Is 2 1 ˆ (1/ ) n i i Y n Y unbiased for θ ? In addition, (c) Find 1 ˆ Var( ) and 2 ˆ Var( ) . (d) Is 1 ˆ or 2 ˆ a better estimator for ? Why?

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