1. (5{.)pts)An entrepreneurial engineering student decides to make some extra money by making shorthaul 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 Xi be a random variable that represents the student's location in the morning before the rst 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 X}: take on the values 1 (Austin), 2 (Brenham), or 3 ( .lollege Station). Historical data. for daily starting and ending locations over the past 2 years is shown below. Start Austin Brenham 3.8. *0' Austin 15 45 30 La Brenham fit} 25 40 IS . 25 30 30 (a) Dene the Markov chain model for the student's starting location. Include the transition matrix and transition diagram. (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 2(.}% chance of starting in Brenham and a 80% chance of starting in (1) Jollege Station, calculate p2 . What is the interpretation of this value