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Let {N1(t),t ≥ 0} and {N2(t),t ≥ 0} be two independent Poisson processes, with rates λ1 and λ2, respectively. We defineN(t) = N1(t) - N2(t).
(a) Explain why the stochastic process {N(t) t ≥ 0} is not a Poisson process.
(b) Give a formula for the probability P[N(t2) - N(t1) = n], for t2 > t1 ≥ 0 and n ∈ { 0 , ± 1 , ± 2 , . . . }.
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