If X 1 is the mean of a random sample of size n from a normal population
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If X̅1 is the mean of a random sample of size n from a normal population with the mean µ and the variance σ21, X̅2 is the mean of a random sample of size n from a normal population with the mean µ and the variance σ22, and the two samples are independent, show that
(a) ω ∙ X̅1 +(1 – ω) ∙ X̅2, where 0 ≤ ω ≤ 1, is an unbiased estimator of µ;
(b) The variance of this estimator is a minimum when
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Related Book For
John E Freunds Mathematical Statistics With Applications
ISBN: 9780134995373
8th Edition
Authors: Irwin Miller, Marylees Miller
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