Suppose that $X$ and $Y$ are exponential r.v.'s with parameters $\lambda$ and $\mu$. Given the condition that $X$ is bounded by $Y$ (i.e., $X<Y$), how do I find the probability that a number $t$ falls between $X$ and $Y$?
Can I interpret this question as $P(X<t<Y\mid X<Y)$? If correct, how to compute it?
A follow-up question. Given the condition that $X<Y$ and $t<Y$, how do I compute the probability that $X<t$?