2. Suppose we have a i.i.d sample X1, X2, ..., Xn, with E(Xi) = u, and Var(X;) = -, i = 1, 2, ..., n. Recall: X = 71 Xi We know that the sample mean X is an unbiased estimator of u. Now suppose that I flip a fair coin (i.e. P(H) = P(T) = 1/2), and I propose a new estimator for the population mean u. This new "gambler's estimator" for the mean is given by: X = X+D where D = +1 if the flip is heads and D = -1 if the flip is tails. a. Is X an unbiased estimator for the population mean u? Explain. b. Would it still be unbiased if the coin was not fair? c. Compute the variance of the X estimator. d. Which one is a better estimator of u, X or the "gambler's one? Explain why