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

38. Let {Mi(t),t 0}, i = 1, 2 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)

.