Q41Section I (Objective (Q1–Q80))41 of 80

Sufficient statistic — discrete uniform

Let $x_1,x_2,\dots,x_n$ be independent random variables each having the distribution $\mathbb{P}(x_i=k)=\dfrac1N; k=1,2,\dots,N; N\in Z$ , the set of positive integers. If $x_{(n)}=\max(x_i)$ and $x_{(1)}=\min(x_i)$ , then the sufficient statistic for the parameter $N$ is:

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