Suppose that {N1(t), t ≥ 0} and {N2(t), t ≥ 0} are independent Poisson processes
with rates λ1 and λ2. Show that {N1(t) + N2(t), t ≥ 0} is a Poisson process with
rate λ1 + λ2. What is the probability that the first event of the combined process
comes from {N1(t), t ≥ 0}?