Let X1,X2,…,Xn (nge 2) be a random sample from a distribution with probability density function f(x;theta)=begincasesdfrac3x^2thetae^-x^3/theta,&x00,&otherwiseendcases, where thetain(0,infty) is unknown. If T=displaystylesumi=1^nXi^3, then which of the following statements is/are TRUE?

Q39Section B (Section B)39 of 60

UMVUE and MLE of the inverse scale

Let $X_{1},X_{2},…,X_{n}$ $(n\ge 2)$ be a random sample from a distribution with probability density function $f(x;\theta)=\begin{cases}\dfrac{3x^{2}}{\theta}e^{-x^{3}/\theta},&x>0\\0,&\text{otherwise}\end{cases},$ where $\theta\in(0,\infty)$ is unknown. If $T=\displaystyle\sum_{i=1}^{n}X_{i}^{3}$ , then which of the following statements is/are TRUE?

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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