Please explain in details, and I don't want answers copied from other WEBSITES ANSWERS. Thanks!

Let X1, ..., X, be a random sample from some density which has mean & and variance o2. (a) Show that _ a, X, is an unbiased estimator of u for any set of known constants (1, . . ., an Satisfying Zai = 1. n (b) If _ a, = 1, show that var [ _ a, X,] is minimized for a, = 1, i = 1, ..., n. 1 n n [HINT: Prove that 2 at = [(a: - 1)2 + 1 when > a, = 1.]