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Competitive Stats
Q32Section I (Objective (Q1–Q80))32 of 80

Statistical Inference — sufficient statistic for power family

Let X1,X2,X3,…,XnX_1, X_2, X_3, …, X_n be a random sample from a distribution with pdf f(x,θ)=θxθ−1f(x, \theta) = \theta x^{\theta-1}; 0<x<10 < x < 1, θ>0\theta > 0. Then the sufficient statistic for θ\theta is:

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