1. Suppose that a one-celled organism can be in one of two states-either A or B. An individual in state A will change to state B at an exponential rate α; an individual in state B divides into two new individuals of type A at an exponential rate β. De?ne an appropriate continuous-time Markov chain for a population of such organisms and determine the appropriate parameters for this model.
2. Consider two machines that are maintained by a single repairman. Machine i functions for an exponential time with rate μi before breaking down, i = 1, 2. The repair times (for either machine) are exponential with rate μ. Can we analyze this as a birth and death process? If so, what are the parameters? If not, how can we analyze it?