. In a simple Poisson process, let p„(t)= Pr {N{t) = n\N{0) = 0}. Use the relations

to derive differential-difference equations for n = 0.1,2,..., in the same manner in which (9.8) was derived for the Yule process. Solve the system of equations to recover the Poisson probabilities (9.1).

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1 - + (.), k = 0, Pr{AN(t)=k}=At+o(At), k = 1, o(At), k 2,