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Let X1, ..., Xn be a random sample from a probability density function: f(x; β) =...

Let X1, ..., Xn be a random sample from a probability density function: f(x; β) = βxβ−1 for 0 < x < 1 (where β > 0).

a) Obtain the moment estimator for β.

b) Obtain the maximum likelihood estimator for β.

c) Is each of the estimators of a) and b) a sufficient statistic?

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