Question: 5. Let X1, ..., X15 be independent identically distributed random variables with p.d.f. f(x) = -42 exp(-24/0), where @ > 0, and > 0. a)

5. Let X1, ..., X15 be independent identically distributed random variables

5. Let X1, ..., X15 be independent identically distributed random variables with p.d.f. f(x) = -42 exp(-24/0), where @ > 0, and > 0. a) Find the rejection rule (critical region) of the MP (most powerful) test for H. : 0 = 2 vs. H1 : 0 = 01,01 > 2. (Find the rejection rule in the simplest implementable form.) b) Note that 2x, ~ x. (E[V] = = n and Var[V] = 2n where V ~ xa.) If the significance level a = 0.05, determine explicitly the constant value in the rejection region using the table below. c) What is the approximate power (probability of rejecting Ho) of your MP test at 01 = 5? d) Is your MP test also a uniformly most powerful (UMP) test for testing Ho : 0 = 2 vs. H1:0 > 2? Give reasons. The tabled values below give qdf,a where P(xs 0, and > 0. a) Find the rejection rule (critical region) of the MP (most powerful) test for H. : 0 = 2 vs. H1 : 0 = 01,01 > 2. (Find the rejection rule in the simplest implementable form.) b) Note that 2x, ~ x. (E[V] = = n and Var[V] = 2n where V ~ xa.) If the significance level a = 0.05, determine explicitly the constant value in the rejection region using the table below. c) What is the approximate power (probability of rejecting Ho) of your MP test at 01 = 5? d) Is your MP test also a uniformly most powerful (UMP) test for testing Ho : 0 = 2 vs. H1:0 > 2? Give reasons. The tabled values below give qdf,a where P(xs

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