# Problem of the Week #82 - December 23rd, 2013

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#### Chris L T521

##### Well-known member
Staff member
Here's this week's problem.

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Problem: Let $X$ and $Y$ be independent exponential random variables with respective rates $\lambda$ and $\mu$. Argue that, conditional on $X>Y$, the random variables $\min(X,Y)$ and $X-Y$ are independent.

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