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Q38Section I (Objective (Q1–Q80))38 of 80

Statistical Inference — sufficient statistic for a power distribution parameter

Let x1,x2,x3,…,xnx_1, x_2, x_3, …, x_n denote a random sample from a distribution with pdf f(x;θ)={θxθ−1,0<x<1 0,elsewheref(x; \theta) = \begin{cases}\theta x^{\theta - 1}, & 0 < x < 1 \ 0, & \text{elsewhere}\end{cases}, where θ>0\theta > 0. The sufficient statistic for θ\theta is

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