Question: 4. Let X1, X2, Xn be a random sample from the normal distribution with known mean but with the variance as the unknown parameter.

4. Let X1, X2, Xn be a random sample from the normal distribution with known mean but with the variance as the unknown parameter. Hint: write out the density in terms of v = 0. a. Find the information in a single observation and the Cramer-Rao lower bound. b. Find the mle of . c. Find the distribution of the mle. Hint: The sum of squares of n independent standard normal random variables follows a 22 distribution. Xn d. Is the mle an efficient estimator? Hint: The mean of a X2-2 random variable is n and the variance is 2n. n

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