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Question 2 (35 points) An auto insurance company classifies its customers (policyholder's) into three categories: Poor, satisfactory and preferred. A policyholder's category may change at the time of a renewal in response to the number of claims made by that policyholder during the previous policy period. a) (5 points) Explain why the category of a policyholder may change randomly over time. b) (5 points) Identify the epochs in the above situation. c) (10 points) Which method is appropriate to progress the time in the discrete time stochastic model of the above situation? Explain. d) (5 points) Define Xn and write down the state space S. 4 e) (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