Two surveys were independently conducted to estimate a population mean, μ. Denote the es...

Two surveys were independently conducted to estimate a population mean, μ. Denote the estimates and their standard errors by .

Assume that are unbiased. For some α and β, the two estimates can be combined to give a better estimator:

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 unbiasedness?