Suppose that X 1 , , X n form a random sample from a Normal distribution for which mean is known, but the variance 2 is unknown Find the MLE ( maximum likelihood estimation )for 2 Is the MLE a UMVUE ( uniformly minimum variance unbiased estimator) for 2 If not, what is the modified version of the MLE such that it is UMVUE for 2

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Question: Suppose that X 1 , . . . , X n form a random sample from a Normal distribution for which mean is known, but

Suppose that X₁, . . . , X_n form a random sample from a Normal distribution for which mean is known, but the variance ² is unknown. Find the MLE (maximum likelihood estimation)for ².Is the MLE a UMVUE (uniformly minimum-variance unbiased estimator)for ²? If not, what is the modified version of the MLE such that it is UMVUE for ²?

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