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QUESTION
Let {N1 (t), t 0} and {N2 (t), t 0} be two independent, time homogeneous Poisson processes with constant rate 1 and 2 respectively.
Let {N1 (t), t ≥ 0} and {N2 (t), t ≥ 0} be two independent, time homogeneous Poisson processes with constant rate λ1 and λ2 respectively. Then, for a fixed time point t, the distribution of the random variable N1 (t) + N2 (t) is what?
Is it is a poisson process, if yes then with what parameters?
