7. (Rejection Region, 5+5=10 points) Let 11, 12, ..., In are samples from Rayleigh Distribution Ra(0), and the probabili

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7 Rejection Region 5 5 10 Points Let 11 12 In Are Samples From Rayleigh Distribution Ra 0 And The Probabili 1 (46 KiB) Viewed 120 times

7. (Rejection Region, 5+5=10 points) Let 11, 12, ..., In are samples from Rayleigh Distribution Ra(0), and the probability density function is as follows: 2.C exp en => 0 42 42 { p(x) = (0 > 0) 0, x <0 72 We construct a test statistics as follows: T = Σ? i=1 2 (a) Please use the test statistics above to find the rejection region of hypothesis test problem: H: 0 = 1 VS H: 01 with siginificance level of 5%. (Hint: Please first verify that -T is the unbiased estimation of o2, and then find the rejection region according to the definition of rejection region.) (b) We assume the volume of samples are large enough, please find the approximate rejection region by using Central Limit Theorem. n (Hint : When X ~Ra(®), X? » Exp (m) 42