Question: Intermediate Statistical Theory: Bayesian estimation Problem 1 Let X1, ..., Xn be an i.i.d. sample from the distribution with probability density function 2x f (x

Intermediate Statistical Theory: Bayesian estimation

Problem 1 Let X1, ..., Xn be an i.i.d. sample from the distribution with probability density function 2x f (x | 0) = 02 exp A2 for x > 0, where 0 > 0. (a) Find the maximum likelihood estimator of 0. Carefully show that it is a maximum. [5] (b) Find the approximate large-sample variance of the estimator. You can use the result that E(X?) = 02 without proving it. [2]

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