Let {N(t): t≥0} be a Poisson process of rate λ.
We are given that for a fixed t, N(t)=n.
Let Ti be the time of the ith event, i=1,2,...,n.
Then the event {T1≤t1, T2≤t2,...,Tn≤tn, and N(t)=n} occurs if and only if exactly one event occurs in each of the intervals [0,t1], (t1,t2]...