Consider a Poisson counting process with arrival rate . (a) Suppose it is observed that there is

Question:

Consider a Poisson counting process with arrival rate λ.
(a) Suppose it is observed that there is exactly one arrival in the time interval [0, to]. Find the PDF of that arrival time.
(b) Now suppose there were exactly two arrivals in the time interval [0, to]. Find the joint PDF of those two arrival times.
(c) Extend these results to an arbitrary number, n, of arrivals?