Let {N(t), t 0} be a Poisson process with rate , and let P0(t) = P(N(t)

Let {N(t), t ≥ 0} be a Poisson process with rate λ, and let P0(t) = P(N(t) =

0). This exercise gives another way to determine P0(t).

(a) Show that P0(t + h) = P0(t)(1 − λh)+o(h).

(b) Derive a differential equation satisfied by P



0(t).

(c) Solve to obtain P0(t).