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Question regarding likelihood ratio and hypothesis testing:

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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?

Top Answer

(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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