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Unformatted text preview: fሺxሻ ൌ ଵ ሺሻஒ ಉ x ିଵ e ି ౮ ಊ , x 0 , where α, β 0 are parameters. Assume that α is known. (1) Find the MLE of β . (2) Is the MLE from(1) a sufficient statistics for β . Justify your answer. (3) Find the MLE of ଵ ஒ . 6. Show that the mean of the a random sample of size n is a minimum variance unbiased estimator of the parameter λ of a Poisson distribution. 7. Let X ଵ , X ଶ , … , X ୬ be a random sample of size n from Nሺµ, 9ሻ . (1) Construct the most powerful test for testing H : µ ൌ 0 vs H ଵ : µ ൌ 1 . (2) Show that the test is the uniformly most powerful test for testing H : µ ൌ 0 vs H ଵ : µ 0 ....
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This note was uploaded on 05/09/2011 for the course DIF 1486 taught by Professor Yow-jenjou during the Spring '11 term at National Chiao Tung University.
- Spring '11