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Distributionshard
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Let X1,X2,…,XnX_1, X_2, \dots, X_nX1​,X2​,…,Xn​ be a sample from a distribution with PDF f(x;θ)=θxθ−1f(x; \theta) = \theta x^{\theta - 1}f(x;θ)=θxθ−1 for x∈(0,1)x \in (0, 1)x∈(0,1) and θ>0\theta > 0θ>0. Which of the following is the complete sufficient statistic for θ\thetaθ?