2. Let Y, Y2, Y3, Y and Y5 be iid (, 0). Let = 1 Yt. t=1 (a) What are the expected value and variance of Y? (b) Now, consider a different estimator of : W What are the expected value and variance of W? (e) Find Var (Wa). (f) For any - numbers ai, (c) Which estimator of do you prefer? Fully justify your answer. n i=1 Let Y, Y2, Y3,,, Yn ~ iid (, 0) and let = Y. As we discussed in class, if more than one estimators are unbiased, we can compare their variances (in general, MSE) to pick a better point estimator. One related comcept is the best linear unbiased estimator (BLUE). (d) Define the class of linear estimator of by Y+ Y+ i = 1, where as are constants. What restriction on the as is need for W to be an unbiased estimator of u? ... n Y3 + W = a;Y a i=1 Y 2 n, the following inequality holds n n 1 () se Ai a. n i=1 i=1 Use this (and above results) to show is the best linear unbiased estimator (BLUE).