A landlord has two rooms for rent, and each room can only be occupied by one tenant. Suppose that the amount of time it takes to find a tenant for either room is exponentially distributed with a mean of 1.5 months, and that the time each tenant lives in their room is exponentially distributed with an average of 6 months. When both rooms are available, the landlord will look for tenants for both rooms at the same time. (a) Let X(t) be the number of rooms occupied. Is {X(t) : t 0} a birth and death process? If so, give the birth and death rates. If not, carefully explain why. (b) Find the long-run proportion of time that both rooms are occupied