Let X1, X2, X3, X4 be a random sample from a continuous distribution with the probability density function f(x)=1/2e^-x-theta, xinR, where thetainR is unknown. Let the corresponding order statistics be denoted by X(1) < X(2) < X(3) < X(4). Then which of the following statements is/are true?

Q39Section B (Section B)39 of 60

MLE and sufficiency for Laplace location

Let $X_1, X_2, X_3, X_4$ be a random sample from a continuous distribution with the probability density function $f(x)=\frac{1}{2}e^{-|x-\theta|}, x\in\mathbb{R}$ , where $\theta\in\mathbb{R}$ is unknown. Let the corresponding order statistics be denoted by $X_{(1)} < X_{(2)} < X_{(3)} < X_{(4)}$ . 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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