Q12Section I (Objective (Q1–Q80))12 of 80

Definition of sufficiency

Let $x_1,x_2,\dots,x_n$ be a random sample from a distribution with p.d.f. or p.m.f. $f(x,\theta)$ , $\theta\in\Theta$ . A statistic $T=(x_1,x_2,\dots,x_n)$ is said to be sufficient for $\theta$ , iff the conditional distribution of $X$ , given $T=t$ , is:

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