Question: Let X be N(0, 0), 0 Let X be N(o, 0), O < O < 00. (a) Find the Fisher information I (0). [5 marks]

Let X be N(0, 0), 0

Let X be N(o, 0), O < O < 00. (a) Find the Fisher information I (0). [5 marks] (b) Let XI,. , Xn be a random sample from this distribution. Find the maximum likelihood estimator for 0. (c) Show that the MLE of 0 is an effcient estimator of 0. (d) What is the asymptotic distribution of VFL(D 0)? [5 marks] [5 marks] [5 marks]

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