Let {N(t), t [0,)} be a Poisson process with rate . Show the following: given that N(t) = n, the n arrival times have

Let {N(t), t ∈ [0,∞)} be a Poisson process with rate λ. Show the following: given that N(t) = n, the n arrival times have the same joint CDF as the order statistics of n independent Uniform(0, t) random variables. To show this you can show that

n! fT, T2, Tn N(t)-n (t1, t2,..., tn) = th 3 for 0 < t