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Let X1, X2, . . . , Xn be iid random variables with pdf f(x|θ) =...

Let X1, X2, . . . , Xn be iid random variables with pdf

f(x|θ) = θx^(θ−1) , 0 < x < 1, θ > 0.

Is there an unbiased estimator of some function γ(θ), whose variance attains the Cramer-Rao lower bound?

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