Let Xâ‚, Xâ‚‚, ..., Xâ‚™ be a sample from a distribution with density function f(x|θ) = θx^(θ-1), 0 < x < 1 and zero otherwise, where θ > 0. Find a sufficient statistic for θ.
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First, we write down the joint density function of the sample: $$ f(\boldsymbol{x}|\theta) = \prod_{i=1}^n f(x_i|\theta) = \prod_{i=1}^n \theta x_i^{\theta-1} = \theta^n \prod_{i=1}^n x_i^{\theta-1} $$ Show more…
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