(b) Briefly explain the following properties (no more than two sentences for each) of a continuous time Markov chain {X(t) : t > 0} with states {0,1,2,...}. Note: you are allowed to utilise some mathematical formulas to help you explain (where applicable). (4 marks) (1) Markov property; (2) Stationary transition probability; (3) Independent increment. (c) State whether the following stochastic processes are measured in discrete or con- tinuous time with discrete or continuous state space. (e.g. Poisson process is measured in continuous time with discrete state space.) (4 marks) (1) Branching process; (2) Brownian bridge; (3) Random walk; (4) Birth and death process.