Consider the simple linear regression problem Yi = 0 1xi i, i = 1, . . . , n where the fixed and known xi satisfy n i=1 xi = 0 and that i N(0, 2) are independent and identically distributed with known variance 2. The regression parameters 0 and 1 are unknown. (a) Write down an expression for the maximum likelihood estimator of 0 and 1. (b) Suppose that we are interested in estimating = 2 1 . Write down an expression for the MLE of . (c) Calculate the bias of the MLE MLE for estimating . In other words, the MLE is not unbiased! (d) Modify the MLE MLE and derive an unbiased estimator for . Call this estimator MOD. (e) Determine which of the MLE and MOD is preferable from the perspective of minimizing the mean squared error