Let X1 and X2 be i.i.d. random variables having the common probability density function f(x)=begincases e^-x, & xge 0, 0, & otherwise. endcases Define X(1)=minX1, X2 and X(2)=maxX1, X2. Then, which one of the following statements is FALSE?

Q11Section A (Section A)11 of 60

Distribution of exponential order statistics

Let $X_1$ and $X_2$ be i.i.d. random variables having the common probability density function $f(x)=\begin{cases} e^{-x}, & x\ge 0, \ 0, & \text{otherwise.} \end{cases}$ Define $X_{(1)}=\min\{X_1, X_2\}$ and $X_{(2)}=\max\{X_1, X_2\}$ . Then, which one of the following statements is FALSE?

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