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This might be an easy question but currently I'm fighting over it with our TA who gave it in the final exam.

Let $X, Y$ random variables and define $Z= \max \{X, Y\}$ what is the distribution of $Z \mid \{X > Y\}$?

Should be $Z\mid \{X>Y\}\sim X$, right?!

Thank you all.

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    I dislike phrasing this as "the distribution of $Z\mid\{X>Y\}$", because students misconstrue it as "the distribution of $\Big( Z\mid\{X>Y\}\Big)$", as if there were a thing called $Z\mid\{X>Y\}$ whose distribution is sought. It's actually $\Big( \text{the distribution of }Z \Big) \mid\{X>Y\}$.2012-05-09

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