I have the following question: Assuming that $X$ and $Y$ are two independent discrete random variables and $\mathrm{Pr}(X \leq Y)$ is known, how easily one can compute the following probability: $\mathrm{Pr}(X \leq Y + Z)$, where $Z$ is a another discrete random variable. It is also known that $Y$ and $Z$ are dependent. I think this makes things a bit complicated .
Do you have any ideas? Bogdan.