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If 1 is the mean of a random sample of

If 1 is the mean of a random sample of size n from a normal population with the mean µ and the variance σ21, 2 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 ∙ 1 +(1 – ω) ∙ 2, where 0 ≤ ω ≤ 1, is an unbiased estimator of µ;

(b) The variance of this estimator is a minimum when

(a) ω ∙ 1 +(1 – ω) ∙ 2, where 0 ≤ ω ≤ 1, is an unbiased estimator of µ;

(b) The variance of this estimator is a minimum when

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