Second Midterm 2000

Second Midterm 2000 - Second Midterm AEB 6933 1. Derive the...

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Second Midterm AEB 6933 1. Derive the maximum likelihood estimator for λ in the exponential distribution () x e x f λ 1 1 = (This derivation should include explicit derivation of the likelihood function). Using the data in column 1 of the data table, estimate λ . 2. Using the results from question (1) test for the hypothesis that 8< λ<9. 3. Derive the method of moments estimator for λ for the exponential distribution in equation (1). 4. What is the asymptotic distribution of the maximum likelihood estimate of λ in question (1)? How do you justify this distribution? 5. Using column 2 in the data table and assuming that the random variable is normally distributed, what is the .05 confidence interval around the sample average? What is the difference between assuming that the variance is known versus unknown?
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Table 1. Test Data (1) (2) (3)=(2) 2 1 11.3850 9.2765 86.0535 2 10.0422 7.1405 50.9868 3 7.2711 9.4056 88.4652 4 25.8137 8.1577 66.5485 5 0.9803 15.1388 229.1827 6 12.3170
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This note was uploaded on 07/18/2011 for the course AEB 6933 taught by Professor Carriker during the Fall '09 term at University of Florida.

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Second Midterm 2000 - Second Midterm AEB 6933 1. Derive the...

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