For each of the following distributions, let X1,..., Xn be a random sample. Is there a function

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For each of the following distributions, let X1,..., Xn be a random sample. Is there a function of θ, say g(θ), for which there exists an unbiased estimator whose variance attains the Cramer-Rao Lower Bound? If so, find it. If not, show why not.
(a) f(x|θ) = θxθ-1, 0 < x < 1, θ > 0
(b) f(x|θ) = log(θ)/θ-1 θx, 0 < x < 1, θ > 1
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Statistical Inference

ISBN: 978-0534243128

2nd edition

Authors: George Casella, Roger L. Berger

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