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Question regarding likelihood ratio and hypothesis testing: ATTACHMENT PREVIEW Download attachment Screen Shot 2019-11-30 at 12.09.38 AM.png 3. Uniform or peaked? You observe data X1, ..., X, lying in the interval [0, 1]. You want to test Ho : X1, .... X, &quot; Uniform[0, 1] against H1 : X1, ..., X, drawn i.i.d. with density f(x) = 6x(1 -x) on r E [0, 1]. (a) What is the likelihood ratio? (b) Suppose that n = 1. Suppose we set a threshold c = 1 for the likelihood ratio. Let X be the one data point observed. What is the range of X values such that you would choose Ho, and what is the range of X values such that you would choose H1? (c) Continuing for the case n = 1, what is the Type I error and the Power of this likelihood ratio test?

(a) The likelihood ratio is ( X 1 , . . . , X n ) = L H 1 ( X 1 , . . . , X n ) L H 0 ... View the full answer

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