Hw8_2700_s09 - 2 . (b) Find the MLE of . (c) Discuss how...

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ENGRD2700 Basic Engineering Probability and Statistics Spring 2009 Homework 8: Point Estimation and Confidence Intervals. Hand in by 1:30 pm on Friday, April 3 in the ENGRD2700 dropbox. Be sure to write your name and section number (1–6) on your homework. Make sure that your homework pages are stapled together. This homework has 10 parts. NOTE: Your answers will be graded on the clarity of your writing as well as the correctness of the answer. You must show your work to receive full credit. Any work that you submit must be your own. 1. Devore (7e) Text: 6.15 (p. 242) 2. Let X 1 ,...,X n be iid with one of two pdfs. If θ = 0, then f ( x | θ ) = 1 for 0 < x < 1 (and 0 otherwise). If θ = 1, then f ( x | θ ) = 1 / (2 x ) for 0 < x < 1 (and 0 otherwise). Find the MLE of θ . 3. Devore (7e) Text: 6.20 (p. 251) 4. Devore (7e) Text: 6.22 (p. 251) 5. Devore (7e) Text: 6.28 (p. 251) 6. One observation, X , is taken from a N (0 2 ) population. (a) Find an unbiased estimator of
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Unformatted text preview: 2 . (b) Find the MLE of . (c) Discuss how the method of moments estimator of might be found. 7. Devore (7e) Text: 7.4 (p. 262) 8. Devore (7e) Text: 7.6 (p. 262) 9. An engineer reports that in a sample of 50 microdrills drilling a low-carbon alloy steel, the average lifetime (expressed as the number of holes drilled before failure) was 12.68 with a standard deviation of 6.83. (a) Find an approximate 95% condence interval for the mean lifetime of microdrills under these conditions. (b) Based on the same data, another engineer previously reported an approximate condence interval of (11.09, 14.27), but neglected to specify the level. What is the level implied by this condence interval. (c) Find an approximate 99% upper condence bound for the mean lifetime of microdrills. 10. Devore (7e) Text: 7.32 (p. 276)...
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This note was uploaded on 04/05/2009 for the course ENGRD 2700 taught by Professor Staff during the Spring '05 term at Cornell University (Engineering School).

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