4) Suppose X] and X; are independent random variables with the same unknown mean ux. Both X1 and X2 have variance of 64. Let T=aX1 + ng be an estimator of \"X, where a and b are constants. a) Show that, if a+b=l, T is an unbiased estimator of ux. b) If a=% and b=%, what is the variance of T? c) If a='/2 and b='/2, what is the variance of T? d) What choice of a and b minimizes the variance of T, subject to the requirement that T be an unbiased estimator of ux? (Hint: Find the variance of T and use the fact that T is unbiased to write the variance in terms of only a. Then nd the value of a that minimizes the variance.)