Question

In: Statistics and Probability

Let X1,...,Xn be i.i.d. N(θ,1), where θ ∈ R is the unknown parameter. (a) Find an...

Let X1,...,Xn be i.i.d. N(θ,1), where θ ∈ R is the unknown parameter.

(a) Find an unbiased estimator of θ^2 based on (Xn)^2.

(b) Calculate it’s variance and compare it with the Cram ́er-Rao lower bound.

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