If $\{Nt\}t ≥ 0$ is a Poisson process with intensity $λ > 0$, and $T1 < T2 < ...$ etc be the times of the first, second, etc. arrivals. How can I find the conditional density of $T2$ given that $T3 = 1$? What about the conditional density of $T2$ given that $N1 = 2$?
I've set up: $P(T2< x | T3=1) = P(T2 < x \cap T3=1)/P(T3=1)$ for the first part, but I'm not sure where to go from there, and I'm not sure how to set up the second part either.
[self-study]tag & read its wiki. Then tell us what you understand thus far, what you've tried & where you're stuck. We'll provide hints to help you get unstuck. $\endgroup$