A car plant produces about one hundred cars per day independently of any other day with probabilities as given below. Cars per day 98 | 99 | 100 | 101 Probability 102 0.1 0.2 | 0.4 | 0.2 | 0.1 A train with space for one hundred cars collects finished cars from the plant at the end of each day. if four or more cars remain, a road transporter is used to carry four cars to the depot. If three or fewer cars remain, then these cars are held for collection the following day. (a) Explain why the number of cars held over each night can be mod- elled as a Markov chain with state space S = {0, 1,2, 3}. (b) What is the transition matrix for this Markov chain?

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