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Competitive Stats
Q9Section I (Objective (Q1–Q80))9 of 80

Statistical Inference — sufficient statistic for a power-law shape parameter

Let X1,X2,X3,...,XnX_1, X_2, X_3, ..., X_n be a random sample from a population with pdf f(x,θ)=θxθ−1f(x,\theta)=\theta x^{\theta-1}; 0<x<10<x<1; θ>0\theta>0. The sufficient statistic for θ\theta using factorization theorem will be

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