# 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?

(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?

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