Question: Consider two independent Poisson processes with the same parameter . Let Ni(t) ,i = 1, 2 be the number of events in ith process which

Consider two independent Poisson processes with the same parameter λ. Let Ni(t) ,i = 1, 2 be the number of events in ith process which occurred up to time t, and let UT be the set of all those times t with 0≤ t ≤ T at which N1(t) = N2(t).

Find E(UT ) given that: (i) N1(T) = N2(T)=2. (ii) N1(T)=2,N2(T)=3. (Hint:

Use the fact that the sum of two independent Poisson processes is a Poisson process and Theorem 9.8.5.)

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