Let {N(t), t ≥ 0} be a nonhomogeneous Poisson process with intensity function λ(t), trend function Λ(t) =  and arrival time point T i of the ith Poisson event. Show that, given N(t) = n, the random...

Let {N(t), t ≥ 0} be a nonhomogeneous Poisson process with intensity function λ(t), trend function Λ(t) =
 and arrival time point T_i
of the ith Poisson event. Show that, given N(t) = n, the random vector (T₁, T₂, ..., T_n) has the same probability distribution as n ordered, independent, and identically distributed random variables with distribution function

Hint Compare to theorem 3.5.