Five mercedes e550 vehicles are shipped to a local dealership. the dealer sells one e550 in any week with probability 0.3 and otherwise sells none in that week. when all e550s in stock have been sold, the dealer requests a new shipment of five such cars, and it takes 1 week for that delivery to occur. let xn = 1/4 the number of mercedes e550s at this dealership n weeks after the initial delivery of five cars.
(a) construct the transition matrix for this chain. [hint: the states are 0, 1, 2, 3, 4, 5.]
(b) determine the steady-state probabilities for this chain.
(c) on the average, how many weeks separate successive orders of five e550s?