Question

STATISTICS

Let (X_{1},X_{2},...,X_{n}) be a simple random sample of a given random variable X with density function

f\left ( x\mid \theta \right )= \frac{1}{\theta }x^{\frac{1}{\theta }-1} , , 0< x< 1 ,  \theta > 0

Calculate a sufficient statistic for \theta and an unbiased estimator  for \theta which is function of the previous sufficient statistic.

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