Question: Let X be a random variable with mean μ and variance σ2. Given two independent random samples of sizes n1 and n2, with sample means

Let X be a random variable with mean μ and variance σ2. Given two independent random samples of sizes n1 and n2, with sample means X1 and X2, show that

is an unbiased estimator for . If X1 and X2 are independent, find the value of a that minimizes the standard error of X.

X = aX, + (1 a)X. 0 < a

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