Let X1,X2,…,Xn (nge2) be a random sample from a distribution with the probability density function f(xtheta)=begincasesdfrac xtheta^2e^-x/theta, & x0, 0, & otherwise,endcasesquadtheta0. Let overline X=frac1nsumi=1^nXi. Which of the following statistics is (are) sufficient but NOT complete?

Q39Section B (Section B)39 of 60

Sufficient but not complete statistics for a gamma family

Let $X_1,X_2,…,X_n$ ( $n\ge2$ ) be a random sample from a distribution with the probability density function

$f(x|\theta)=\begin{cases}\dfrac x{\theta^2}e^{-x/\theta}, & x>0,\ 0, & \text{otherwise,}\end{cases}\quad\theta>0.$

Let $\overline X=\frac1n\sum_{i=1}^nX_i$ . Which of the following statistics is (are) sufficient but NOT complete?

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.

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