hw9 - the hypothesis H : v.s. the alternative H A :...

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1. textbook, Chapter 9, p.363, problem 7. [Hint: apply Neyman-Pearson lemma.] 2. textbook, Chapter 9, p.363, problem 8. [Hint: Example 7.9 in LNp.19.] 3. textbook, Chapter 9, p.366, problem 29. 4. textbook, Chapter 9, p.366, problem 30. 5. Let X 1 ,...,X n be i.i.d. with pdf f which can be either f 0 or else f 1 , where f 0 is Poisson P (1) and f 1 is the Geometric pdf with p = 1 2 . Find the most powerful (MP) test of the hypothesis H 0 : f = f 0 v.s. the alternative H A : f = f 1 at level of significance 0.05. [Hint: apply Neyman-Pearson lemma and construct a randomized test] 6. Let X 1 ,...,X n be independent random variable with pdf f given by f ( x | θ ) = 1 θ e - x θ , for x 0, where θ Ω = (0 , ). Derive the uniformly most powerful (UMP) test for testing
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Unformatted text preview: the hypothesis H : v.s. the alternative H A : < at level of signicance . [Hint: Question 7.10 in LNp.23, and notice that X 1 + + X n follows a Gamma distribution] 7. Let X 1 ,X 2 ,X 3 be i.i.d. from Binomial B (1 ,p ). Derive the uniformly most powerful unbiased (UMPU) test for testing the hypothesis H : p = 0 . 25 v.s. the alternative H A : p 6 = 0 . 25 at level of signicance . Determine the test for = 0 . 05. [Hint: Let Y B (3 , . 25), then P ( Y = 0) = 0 . 42, P ( Y = 1) = 0 . 42, P ( Y = 2) = . 14, and P ( Y = 3) = 0 . 02] 1...
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This note was uploaded on 03/11/2011 for the course STA 506 taught by Professor Lisa during the Spring '11 term at West Chester.

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