Question: This is from Statistical Inference Course, MM is Method of Moments, MLE is Maximum Likelihood Estimator 1. Assume that X1, ..., X, are i.i.d. Gamma(3,

This is from Statistical Inference Course, MM is Method of Moments, MLE is Maximum Likelihood Estimator

1. Assume that X1, ..., X, are i.i.d. Gamma(3, A), where A > 0. (a) Find a one-dimensional sufficient statistics. (b) Find the MM estimator. (c) Find the MLE. (d) Is the MLE estimator you derived unbiased? What is its MSE? (e) Assuming that the prior is A ~ I(a, b). Find the posterior and the posterior Bayes estimator. (f) Find the CRLB for estimating A

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