Question

Please show your work. Fully characterize all Markov chain models. Thanks!!

1. An entrepreneurial engineering student decides to make some extra money by making short haul trips carrying cargo for customers in Austin, Brenham, and College Station. After a couple of years in business, the student has some fairly robust historical data on demand for cargo services. Let Xt be a random variable that represents the student's location in the morning before the first job of the day on day t. Assume that the student starts each day at the ending location of the evening before. Model the starting location each day using a Markov chain model. Let Xt take on the values 1 (Austin), 2 (Brenham), or 3 (College Station). Historical data for daily starting and ending locations over the past 2 years is shown below Start Austin Brenham C.S Austin25 E Brenham 50 50 30 40 30 20 30 30 C.S (a) Define the Markov chain model for the student's starting location. Include the transition matrix and transition diagranm (b) Is the stationarity assumption reasonable for this model? Why or why not? (c) Describe what the transition probability p31 represents (d) If the student has a 50% chance of starting in Brenham and a 50% chance of starting in College Station, calculate p> What is the interpretation of this value?

Answer 1