Let X1, , Xn be a random sample from a population with mean Icirc frac14 and variance Iuml 2 (a) Show that the estimator is an unbiased estimator of Icirc frac14 if (b) Among all unbiased estimators of this form (called linear unbiased estimators) find the one with minimum variance, and calculate t...

a E i a i X i i a i EX i i a i i a i Hence the estimator is unbiased b Var i a i X i i ...

Let X1,.., Xn be a random sample from a population with mean Î¼ and variance Ï2. (a)

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Let X1,.., Xn be a random sample from a population with mean Î¼ and variance Ïƒ2.
(a) Show that the estimator

is an unbiased estimator of Î¼ if

(b) Among all unbiased estimators of this form (called linear unbiased estimators) find the one with minimum variance, and calculate the variance.

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Statistical Inference

ISBN: 978-0534243128

2nd edition

Authors: George Casella, Roger L. Berger

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Question Posted: May 26, 2016 05:25 AM

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Let X1,.., Xn be a random sample from a population with mean Î¼ and variance Ï2. (a)

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ai = 1. al-

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