Let X 1 ,X 2 , . . .,X n be a random sample from each of
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Let X1,X2, . . .,Xn be a random sample from each of the following distributions involving the parameter θ. In each case find the mle of θ and show that it is a sufficient statistic for θ and hence a minimal sufficient statistic.
(a) b(1, θ), where 0 ≤ θ ≤ 1.
(b) Poisson with mean θ > 0.
(c) Gamma with α = 3 and β = θ > 0.
(d) N(θ, 1), where −∞ < θ < ∞.
(e) N(0, θ), where 0 < θ < ∞.
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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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