Problem 5 Let N₁ (t) and N₂ (t) be two independent Poisson processes with rate ₁ and >₂ respectively. Let N(t) = N₁ (t) + N₂(t) be the merged process. Show that given N(t) N₁ (t) ~ Binomial (n,₁). = Note: 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 12 independent of other arrivals. X₁ +d₂ X₁ + λ2

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