2. Consider a random sample X1,..., Xn from a normal distribution with known mean 0 and unknown variance 0 = o? (a) Write the likelihood and log-likelihood function (b) Derive the maximum likelihood estimator for 0 (c) Show that the Fisher information matrix is I(0) = , (d) What is the variance of the maximum likelihood estimator for 0? Does it attain the Cramer-Rao lower bound?

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.