Let X1,X2,…,Xn be a random sample from a distribution with the probability density function f(x;theta)=begincasesc(theta)e^-(x-theta), & xge2theta, 0, & otherwise,endcases where thetainmathbb R is the unknown parameter. Then which of the following statement(s) is (are) true?

Q38Section B (Section B)38 of 60

MLE when the support depends on the parameter

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

$f(x;\theta)=\begin{cases}c(\theta)e^{-(x-\theta)}, & x\ge2\theta,\ 0, & \text{otherwise,}\end{cases}$

where $\theta\in\mathbb R$ is the unknown parameter. 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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