Question: please help 3- Consider the family with normal distribution N(0, 0). (a) Compute the MLE On for 0 for a sample of size n and

please help

3- Consider the family with normal distribution N(0, 0). (a) Compute the MLE On for 0 for a sample of size n and show that it is an unbiased and consistent estimator for 0. (b) Determine whether or not the statistic On is a sufficient statistic for the family. (c) Explain why non/0 is a x2 distribution, identifying the number of degrees of freedom and use this to compute the variance of On. (d) Compute the Fisher information I(0) and show that the estima- tor 0 is efficient. (e) With n = 5 and a realized value 0(x1, . . ., X5) = 2.3, compute an exact 90% confidence interval for 0

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