Assign1 - p We want to test H p = 1 2 versus H a p 6 = 1 2(a Find the GLRT statistic(b Argue that the critical region from the GLRT is of the

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PSTAT 120C: Assignment # 1 Due April 13, 2006 These problems are due at the start of lecture on Thursday. 1. Show that if T is a sufficient statistic for estimating θ from the data X 1 , . . . , X n then the Generalized Likelihood Ratio Test (GLRT) statistic for testing H 0 : θ Ω 0 versus H a : θ 6∈ Ω 0 is a function of T . (Hint: use the factorization theorem.) 2. Suppose that X is a binomial random variable from n trials with probability
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Unformatted text preview: p . We want to test H : p = 1 2 versus H a : p 6 = 1 2 . (a) Find λ , the GLRT statistic. (b) Argue that the critical region from the GLRT is of the same form as ± ± ± X-n 2 ± ± ± ≥ k α 3. Exercise 10.93 on page 523 in the textbook. 4. Exercises 8.81 and 8.87 on pages 409–410 in the textbook. 5. Exercise 10.67 on pages 505–506 in the textbook. 1...
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This note was uploaded on 04/09/2008 for the course PSTAT 120c taught by Professor Idk during the Spring '07 term at UCSB.

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