What is the approximating distribution of 11 if the prior, Basic Statistics

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What is the approximating distribution of 11 if the prior

Let X1 , Xi , . . . , X" be a random sample from a gamma distribution with a = 2 and P = 1/6, 0 <>6 oo.

(a) Find the m.l.e., 11, of 6. Is 11 unbiased?

(b) What is the approximating distribution of 11?

(c) If the prior distribution of the parameter is exponential with mean 2, determine the Bayes' estimator associated with a square-error loss function.

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