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Estimate the standard errors by the given variables

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Reference no: EM131731652

Question: Two surveys were independently conducted to estimate a population mean, μ. Denote the estimates and their standard errors by X1 and X2 and σX1 and σX2 . Assume that X1 and X2 are unbiased. For some α and β, the two estimates can be combined to give a better estimator:

X = α X1¯ + βX2¯

a. Find the conditions on α and β that make the combined estimate unbiased.

b. What choice of α and β minimizes the variances, subject to the condition of unbiased-ness?

Reference no: EM131731652

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