3. Suppose that ai . ,,an are a random sample from a N( ,02) distribution. Recall that the MLE in this case is [a, _]T = [x, V (n-1)s2/n]T and the information matrix is Consider the data s2-4.84 with n 16 (a) Use the delta-method to obtain an approximate 95% confidence interval for log(o) (b) Obtain an approximate 95% confidence interval for _2 using the confidence interval from (a). Compare to the exact interval, [2.21,15.77], and approximate interval [0.43, 10.50 obtained in class.
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