Suppose that X1, ..., Xn are i.i.d. with N(u, o?) where both u and o MLE are unknown. Let n = exp(2/ + 0?). Let AMLE and o2 be the MLEs of / and o2 respectively. (a) (20 points) Define m = exp(20MLE. ~ MLE + 02 ). Prove or disprove that m is asymp- totically normal, and then find its asymptotic variance. (b) (10 points) Define n2, MLE r((n - 1)/2) n-2 -2 12 = exp(2/1 E j=0 T((n + 2j - 1)/2)j! Prove or disprove that 72 is an unbiased estimator of n