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HW 6 Solutions - so the mle of is Question 32 a for so b...

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STATW1211.005 Prof. Zhang TR 02:40P-03:55P Homework 6 – Solutions Textbook: Probability and statistics for engineering and the sciences (7 th edition) by Jay L. Devore Chapter 6: Question 22 a. , so the moment estimator is the solution to , yielding . Since b. , so the log likelihood is . Taking and equating to 0 yields , so . Taking for each given yields ultimately . Question 27 a. , so the log likelihood is . Equating both and to 0 yields and , a very difficult system of equations to solve. b. From the second equation in a
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Unformatted text preview: , , so the mle of is . Question 32 a. for , so . b. While is not unbiased, is, since . STATW1211.005 Prof. Zhang TR 02:40P-03:55P Chapter 7: Question 8 a. With probability , . These inequalities can be manipulated exactly as was done in the text to isolate ; the result is , so a interval is b. The usual 95% interval has length , while this interval will have length . With and , the length is which is longer. Question 14 a. . Yes, this is a very narrow interval. It appears quite precise. b. ....
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