Let N 1 (t) and N 2 (t) be two independent Poisson processes with rate 1 and 2 respectively. Let N(t) = N

Let N₁(t) and N₂(t) be two independent Poisson processes with rate λ₁ and λ₂ respectively. Let N(t) = N₁(t) +N₂(t) be the merged process. Show that given

We can interpret this result as follows: Any arrival in the merged process belongs to N₁(t) with probability

and belongs to N₂(t) with probability

independent of other arrivals.

N(t) = n, N(t) ~ Binomial n 1+12,