14. Let $ N (t): t 0 % be a Poisson process with rate . By Example 12.38, the process $ N (t): t

14. Let $ N (t): t ≥ 0 % be a Poisson process with rate λ. By Example 12.38, the process $ N (t): t ≥ 0 % is a continuous-time Markov chain. Hence it satisfies equations (12.12), the Chapman-Kolmogorov equations. Verify this fact by direct calculations.