Let X1,X2,…,Xn, where n1, be a random sample from a continuous distribution with probability density function f(x;theta)=begincasestheta x^theta-1& if 0<x<1, 0& otherwise,endcases where theta0 is an unknown parameter. Then which of the following statistics is/are sufficient for theta?

Q38Section B (Section B)38 of 60

Sufficiency for a power family

Let $X_1,X_2,…,X_n$ , where $n>1$ , be a random sample from a continuous distribution with probability density function $f(x;\theta)=\begin{cases}\theta x^{\theta-1}& \text{if }0<x<1,\ 0& \text{otherwise,}\end{cases}$ where $\theta>0$ is an unknown parameter. Then which of the following statistics is/are sufficient for $\theta$ ?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

Keyboard: A–D answer · S solution · ←/→ previous/next