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

Let {Mi(t), t 0},i = 1, 2, 3 be independent Poisson processes with respective rates λi,i = 1, 2, and set N1(t) = M1(t) + M2(t), N2(t) = M2(t) + M3(t)

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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