3. (10 points) Suppose people arrive to a coin-operated telescope at the top of the Eiffel tower in Paris in accordance to a Poisson process with rate 1 = 5 people per hour. Each person is willing to spend an exponentially distributed amount of time with rate u=1 customer per minute using the telescope, but if someone arrives while a person is using the telescope, that person gives the telescope to the new arrival. Model this process as a CTMC, and determine the long-run proportion of time the telescope is being used. 3. (10 points) Suppose people arrive to a coin-operated telescope at the top of the Eiffel tower in Paris in accordance to a Poisson process with rate 1 = 5 people per hour. Each person is willing to spend an exponentially distributed amount of time with rate u=1 customer per minute using the telescope, but if someone arrives while a person is using the telescope, that person gives the telescope to the new arrival. Model this process as a CTMC, and determine the long-run proportion of time the telescope is being used