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Distributionshard
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Let X1,…,XnX_1, \dots, X_nX1​,…,Xn​ be i.i.d. from a distribution with PDF f(x;θ)=θxθ−1f(x; \theta) = \theta x^{\theta-1}f(x;θ)=θxθ−1 on (0,1)(0, 1)(0,1). What is the sufficient statistic for θ\thetaθ?