Sample_Quiz_2 - MLE:C = c B MLE is an unbiased estimator....

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IEOR 165 SPRING 2004 Sample Mid Term Exam (March 11, 2004) Examiner General’s Warning! These are hypothetical questions. They need not be the same or relevant to the actual mid term exam. Answer Both Questions: Q1: Population X has a uniform distribution on (0,b). Suppose we have a random sample X 1 , X 2 ,…., X n of size n. (1) Develop an estimator B MOM for ‘b’ using the method of moments. (2) Find the mean and variance of the above estimator. Is this an unbiased estimator? Otherwise find a constant c such that B MOM:C = c B MOM is an unbiased estimator (3) Obtain the Maximum Likelihood estimator B MLE of ‘b’. (4) Find the mean and variance of the maximum likelihood estimator. Is this unbiased. Otherwise find a constant c such that B
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Unformatted text preview: MLE:C = c B MLE is an unbiased estimator. (5) Which of these four estimators is the best (or the one you would recommend). Explain why? Q2: The viscosity of two different brands of car oil are measured and the following data resulted: Brand 1: 21.24, 21.16, 20.66, 21.44, 20.88, 21.48 Brand 2: 21.00, 21.04, 21.16, 21.24, 21.10, 21.02, 21.06 (1) Test the hypothesis that the mean viscosity of the two brands is equal, assuming that the populations have normal distributions with equal variances. (2) Test the hypothesis that the populations have the same variances. (3) Based on the conclusion you have for part (2) do you consider your test in part (1) valid? If not, carry out the more appropriate test....
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This note was uploaded on 07/22/2009 for the course IEOR 165 taught by Professor Shanthikumar during the Summer '08 term at University of California, Berkeley.

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