Question: Let X be a random variable with mean and variance 2 . Given two independent random samples of sizes n1 and n2, with sample means

Let X be a random variable with mean and variance 2 . Given two independent random samples of sizes n1 and n2, with sample means X 1 and X 2. Let X = aX 1+(1a)X 2, 0 < a < 1 be a point estimator for a) Show that X is unbiased estimator for . b) Find the value of a that minimizes the standard error of X

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