Given the joint density of two random variables $X$ and $Y$,

$f_{XY}(x,y)=2e^{-(x+y)}$ for $0<x<y$

How do I compute $P(Y<1|X=1)$?

I know the conditional probability formula is:


However, I'm unsure about the bounds of the integral


1 Answer 1


The PDF tells us that $X<Y$ a.s. so that $P(Y<1\mid X=1)=0$.

  • $\begingroup$ oh my, I just had a brain fart. Thank you! $\endgroup$
    – i9-9980XE
    Commented May 23, 2019 at 15:23

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