Question: 9.3.12 Consider two independent Poisson processes with the same parameter A. Let Ni ( t ) , i=l, 2 be the number of events in

9.3.12 Consider two independent Poisson processes with the same parameter A. Let Ni ( t ) , i=l, 2 be the number of events in i-th process which occurred up to time t , and let UT be the set of all those times t with 0 5 t 5 T at which N l ( t ) = N2(t).

Find E(&) given that: (i) N l ( T ) = N2(T) = 2. (ii) N l ( T ) = 2 , N 2 ( T ) = 3.

(Hint.U se the fact that the sum of two independent Poisson processes is a Poisson process and Theorem 9.8.5.)

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