At least I think that's the sort of thing the question's aiming at...
John and Jane have arranged to meet at a given time, and each, independently, will be late by an amount of that time that is exponentially distributed with parameter . Let and denote the amount of time that John and Jane are late respectively.
Suppose that we are interested in the length of time that Jane arrives before John, that is, in . For , show that
Seriously do feel like this isn't all that complicated, but I just keep hitting a wall.
I attached the past paper this question comes from - it's question B6, part (b), part (ii).