Let {N(t) : t >=0} be a Poisson process of rate 1 and let denote the times of the points. Derive the pdf of
So I've been trying to work with the distribution function. I have:
I get stuck there though and can't find a similar example.
It may help you to prove that are i.i.d. exponentials (where T_0=0). Now where both and are independent exponentials. Now use the law of total probability and condition one of them.