Let X1,X2,…,Xn be a random sample from a distribution with the probability density function f(x;theta)=begincasestheta^2xe^-theta x, & x0, 0, & otherwise,endcases where theta0 is the unknown parameter. If Y=sumi=1^nXi, then which of the following statement(s) is (are) true?

Q39Section B (Section B)39 of 60

UMVUE of the rate parameter of a gamma family

Let $X_1,X_2,…,X_n$ be a random sample from a distribution with the probability density function

$f(x;\theta)=\begin{cases}\theta^2xe^{-\theta x}, & x>0,\ 0, & \text{otherwise,}\end{cases}$

where $\theta>0$ is the unknown parameter. If $Y=\sum_{i=1}^nX_i$ , then which of the following statement(s) 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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