2002-52.md

course	course_year	question_number	tags	title	year
Statistics	IB	52	IB 2002 Statistics	$1 . \mathrm{I} . 3 \mathrm{H} \quad$	2002

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

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