Answer Happy

Question 2 (35 points) Consider the above situation in which a section of highway is inspected for damage at the end of each year. Based on specific measurements of frequency, and depths of cracks, the highway section is classified to be in one of four possible grades of deterioration: "Good as new" (1). "Minor Deterioration (2). "Usable" (3), and "Unusable" (4). Damage is progressive and eventually the highway section becomes unusable. Once it becomes unusable, the section of the highway is repaired until the next inspection and its' grade becomes "Good as new". Past experience suggests that probability of deteriorating one grade between two inspections is 0.2, and two grades is 0.05. The highway section does not deteriorate three grades between two inspections. a) (5 points) Identify the epochs in the above situation b) (5 points) Which method is appropriate to progress the time in the discrete time stochastic model of the above situation? Why? Explain? c) (10 points) Define Xn and write down the state space S. d) (10 points) Write down the Markov assumption in your own words for the above real-life situation, and comment whether it is realistic or not. e) (5 points) Do you think stationarity assumption makes sense in the above situation? Explain and give an example in which the stationarity assumption would not hold. Write your answers on a sheet of paper, scan it and upload.