5. You conduct a random sample of n = 2 individuals from a population with mean u and variance 02. You know that the sample mean, X = (X1 + X2), would be the typical estimator for the population mean. However, you instead decide to estimate the population mean using a different weighted average of your sample values, X = X1 + 3 X2. 5.1. * (6 points) Show that X is an unbiased estimator of u. 5.2. * (6 points) Find Var(X). 5.3. (3 points) If two unbiased estimators have difference variances, then the estimator with the smaller variance is said to be more efficient. Compared to X, is X more efficient, less efficient, or equally efficient? 2