A Poisson process has intensity $\lambda$. Given $X (t) = n$, derive the conditional density function for the waiting time of the $m$th event, provided $m ≤ n$.
From my textbook, it looks like waiting times are distributed according to the gamma function. I'm a little unsure of how to get started on this. Is this conditional on $X(t)=n$? The wording of these questions is still a little confusing to me. Would appreciate any guidance.