12. Let N(t) : t 0 be a Poisson process with rate . By Example...

12. Let



N(t) : t ≥ 0

be a Poisson process with rate λ. By Example  12.34, the process N(t) : t ≥ 0

is a continuous-timeMarkov chain. Hence it satisfies equations (12.12), the Chapman–Kolmogorov equations. Verify this fact by direct calculations.