Problem 3 (35 points). Suppose that the random variables Y1, . .., Yn satisfy Yi = Bxit Ei, i = 1, ...,n, where x1, . .., In are fixed constants, and E1, . .., En are i.i.d. variables with standard normal distritbution N(0, 1). (1) (10 points) Find the M.L.E., Bn , of B, and show that it is an unbiased estimator of B. (2) (10 points) Define another two estimators On- and On as follows: B(2) _ LizYi n B (3) = _ Yi n i=1 Show that both of them are unbiased. (3) (10 points) Find the relative efficiency of Bn relative to Bn and Bn respectively, i.e., eff( Bn , Bn ) and eff( Bn , B,'). (4) (5 points) Use the M.L.E. to construct a two-sided (1 - a) confidence interval for B