Question: Passengers arrive at a train station according to a Poisson process with rate λ and, independently, trains arrive at the same station according to another Poisson process, but with the same rate λ. Suppose that each time a train arrives, all of the passengers waiting at the station will board the train. Let X(t) = 1, if there is at least one passenger waiting at the train station for a train; let X(t) = 0, otherwise. Let N (t) be the number of times the continuous-time Markov chain $ X(t): t ≥ 0 % changes states in [0, t]. Find the probability mass function of N (t).