(15 points} Consider a shuttle that can carry up to c = 2 riders at a time. Upon arrival at a stop, each individual rider on the shuttle departs from the shuttle with probability 2 f 3 or else remains on the shuttle with probability 1/3. Individual riders depart or remain independent of each other. After any such departures, an independent number of potential new riders arrive, where: PH}: of potential new riders = O} = 0.20 P(# of potential new riders = 2:) = 0.11] for 1: = 1,2, . . . ,3 If there are enough open spots on the shuttle, then all potential new riders board. If there are more potential new riders than open spots, then as many potential new riders board as there are open spots. Any potential new riders who are unable to board simply go away and take another form of transit. The shuttle then leaves the stop. At any given current shuttle stop, if there were 1; people on the shuttle when it left the previous stop, then the number of people onboard when it leaves the current stop will he min { c, i Hf: of riders who depart) + H: of potential new riders) }. Obtain the transition matrix for a Markov chain model for the number of riders on the shuttle as it leaves each stop. Explain your answers (you may wish to use the next page for additional spaoe}