Let X 1 ,X 2 , . . .,X n be a random sample from a distribution
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Let X1,X2, . . .,Xn be a random sample from a distribution with pdf f(x; θ) = θxθ−1, 0 < x < 1, zero elsewhere, where θ > 0. Show the likelihood has mlr in the statistic Πni=1 Xi. Use this to determine the UMP test for H0 : θ = θ' against H1 : θ < θ', for fixed θ' > 0.
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Under H0 the UMP is H0 versus H1 The statistic is then defined as where This will be abbreviated to 1 There are nn12 tests so under H0 and H1 the stat...View the full answer
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Related Book For
Introduction To Mathematical Statistics
ISBN: 9780321794710
7th Edition
Authors: Robert V., Joseph W. McKean, Allen T. Craig
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