Let {Mi (t ), t ≥ 0}, i = 1, 2, 3 be independent Poisson processes with respective rates λi, i = 1, 2, and set

The stochastic process {(N1(t ),N2(t )), t ≥ 0} is called a bivariate Poisson process.

(a) Find P{N1(t) = n,N2(t) = m}.

(b) Find Cov(N1(t ),N2(t)).

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N(t) = M(t)+ M2(t), N2(t) = M2(t) + M3(t)