Question: Question 4 (20 points) Let X1, ..., Xn be a random sample from a N(, ) distribution. (a) (6) Find the maximum likelihood estimators

Question 4 (20 points) Let X1, ..., Xn be a random sample from a N(, ) distribution. (a) (6) Find the maximum likelihood estimators and . Note that you do not need to use derivative tests to prove you have found a maximum. (b) (4) Find the Fisher information matrix J (0) where 0 (, ). (c) (5) State the asymptotic distribution of = (, ). (d) (5) Consider the parameter = +. Find the asymptotic distribution of the corresponding ML estimator 7.

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