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(Solved): please write on paper Let X1 be a sample of size 1 from the uniform distr ...
please write on paper
Let be a sample of size 1 from the uniform distribution on the interval with p.d.f. and unknown parameter (a*) Show that is a complete and sufficient statistic. (b*) Show that and are independent from each other.
Expert Answer
(a) To show that $T=|X_1|$ is a sufficient statistic for $\theta$, we need to show that the conditional distribution of $X_1$ given $T=t$ depends on $\theta$ only through $t$.