Question: 4. (40 POINTS) Let X,,...,X, be a random sample from a distribution with pdf a. Find the MLE for 0. fx (x;0) = 0xe*,

4. (40 POINTS) Let X,,...,X, be a random sample from a distribution with pdf a. Find the MLE for 0. fx (x;0) = 0xe*, x>0, 0>0. b. Find the bias of the MLE from part a. Is it asymptotically unbiased? c. Using MLE theory, show how to use the sample to construct an approximate (1-) 100% confidence interval for 0. d. Repeat c., but this time start with the central limit theorem.

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