Two surveys were independently conducted to estimate a population mean, mu. Denote the estimators and their standard errors by X_1 X_2 and sigma X_1 and sigma X_2. Assume that X_1 and X_2 are unbiased. For some alpha and beta, the two estimators can be combined to give a better estimator: X = alpha X_1 + beta X_2. Find the conditions on a and 0 that make the combined estimator X unbiased. What choice of a and alpha minimizes the variance of beta, subject to the condition of unbiasedness?