Question

Please show all your work and submit one report as a team. To obtain any credit you must show how you obtained the answer even if you used a calculator to actu ally compute it. 1. The ranger's office at the Grand Canyon provides mule trips to people. People in- terested in mule trips wait for a mule in the waiting area. Mules arrive at the waiting area, one by one, in fixed time intervals of every 10 minutes. If nobody is waiting there, the mule departs; otherwise, the mule picks up a single person and leaves. We assume that waiting people are really interested in the mule trips, so they stay in line until it is their turn. Also, the number of people arriving during a ten minute interval is independent of arrivals during previous intervals. We have Plk customers arrive during 10 minute intervall-P for k 2 0, where P0 and Ek Pi 1. Let Xn denote the number of people at the stand at the beginning of the nth time interval (Gust after the mule departs the stand). (a) Express Xn+1 in terms of Xn and show that fX,1 20 is a Markov Chain. (b) Obtain the transition probability matrix (in terms of py's).

Answer 1