Let X1,...,Xn be iid N(μ , σ^2) with μ known and σ^2 unknown. Please carefully re-read...

Let X1,...,Xn be iid N(μ , σ^2) with μ known and σ^2 unknown. Please carefully re-read that sentence, as it is an uncommon setup!

(a) Find the Cramer-Rao lower bound for an unbiased estimator of σ^2.

(b) The MLE for σ^2 is ∑(xi−μ)^2 / n. Find the variance of this estimator. You may find use of the following property: E[(X−μ)^4] = 3σ^4.

c) Find the efficiency of the MLE. Is it a MVUE? Explain.

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Expert Solution

orchestra answered 1 year ago

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