I will attach my question.

Problem 1 (50 points) Consider the model Y = BX+U. where U is independent of X", E(U)=0, E(U') =o', and E(X])=M 0 is a constant. Denote the resulting estimator of B by Ba - a. Obtain an analytic expression for 8, as a function of the Y's and X, 's. b. Find the probability limit of , as n - . Denote this limit by B'. c. Find the asymptotic distribution of n (Ba - B") - d. Find the exact, finite-sample bias, variance, and mean-square error (MSE) of , conditional on the X, 's. e. Is it possible to choose 1 so that , has a smaller MSE conditional on the X 's than the OLS estimator? Prove your result