How can (X|X>Y) change to (X-Y|X>Y)+(Y|X>Y)?
If X~Exp(a), Y~Exp(b), consider (X|X>Y). My book said that (X|X>Y)=(X-Y+Y|X>Y)=(X-Y|X>Y)+(Y|X>Y). But Why?? I don't know why we can divide those two things.
Solution
Stack Overflow doesn't support MathJax/LaTeX to my knowledge so here is an image:
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