1.I.3H1 . \mathrm{I} . 3 \mathrm{H} \quad

Statistics | Part IB, 2002

State the factorization criterion for sufficient statistics and give its proof in the discrete case.

Let X1,,XnX_{1}, \ldots, X_{n} form a random sample from a Poisson distribution for which the value of the mean θ\theta is unknown. Find a one-dimensional sufficient statistic for θ\theta.

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