Example Suppose We Have A Normal Population With Unknown Mean U And Variance 02

Show that both estimators are unbiased for µ. Decide which estimator is more efficient.

Example: Suppose we have a normal population, with unknown mean uand variance 02. We take two observations X1 and X2. selected indepen—dently from this population. _ X XOne choice of an estimator for u is X = $. Another choice of estimator for p, is Y = 2X1 — X2. Show that both estimators are unbiased for u. Decide which estimator ismore efficient.