Suppose that eight observations X1, ..., X8 are drawn at random from a distribution with the following p.d.f. for 0 < x

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Suppose That Eight Observations X1 X8 Are Drawn At Random From A Distribution With The Following P D F For 0 X 1 (49.25 KiB) Viewed 22 times

Suppose that eight observations X1, ..., X8 are drawn at random from a distribution with the following p.d.f. for 0 < x < 1 f(x 0 ) otherwise 5028–1 = Suppose also that the value of 0 is unknown (0 > 0), and it is desired to test the following hypotheses: H : 0 = 1 versus H1:0 = 2. Use Neyman-Pearson lemma to show that the most powerful test (lowest 3) at the level of significance a = 0.05 is to reject Ho if _- In X; >c and the critical value is c= -3.981. Hint: It can be shown that the distribution of Y = -2 In X is xã.f.=2, Chi-squared with 2 d.f.