1. (15 points) Consider the linear regression model with normal errors conditional on the x's: s, ~ iid N(0, 6) a) Recall, the maximum likelihood estimator of B maximizes -SSR(B) = -(y - XB)'( y - XB) Show that the Newton-Raphson algorithm for maximizing -SSR(B) converges in 1 iteration to the least squares estimate B = (X"'X)- X'y regardless of the initial value chosen for the iteration. 2. (25 points) Let X],..., X, be an iid sample with X ~ N(u, o) . Consider the maximum likelihood estimator (mle) of o 62 = - Y ( x, - X ) a) What is the asymptotic distribution of om? b) What is the mle for o ? c) Using the delta method, derive the asymptotic distribution for me Hint: E 0 -2 I(0) = 0 20