Johnson Medical Associates has two physicians on call practicing independently. Each physician is available to answer patients’ calls for independent time periods that are exponentially distributed...

Johnson Medical Associates has two physicians on call practicing independently. Each physician is available to answer patients’ calls for independent time periods that are exponentially distributed with mean 1/λ. Between those periods, the physician takes breaks for independent exponential amounts of time each with mean 1/µ. Suppose that the periods a physician is available to answer the calls are independent of the periods the physician is on breaks. Let X(t) be the number of physicians on break at time t. Show that $ X(t): t ≥ 0 % can be modeled as a birth and death process. Then write down the list of all the Kolmogorov backward equations.