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Let {N1(t), t ≥ 0} and {N2(t), t ≥ 0} be two independent Poisson processes with...

Let {N1(t), t ≥ 0} and {N2(t), t ≥ 0} be two independent Poisson processes with rates λ1 and λ2, respectively. Define N(t) = N1(t) + N2(t). Use the definition to prove that {N(t), t ≥ 0} is a Poisson process with rate λ = λ1 + λ2.

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