1. John travels to work using one of three modes of transport - bicycle, car, or train. The mode of transport he uses on

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1 John Travels To Work Using One Of Three Modes Of Transport Bicycle Car Or Train The Mode Of Transport He Uses On 1 (48.25 KiB) Viewed 28 times

1. John travels to work using one of three modes of transport - bicycle, car, or train. The mode of transport he uses on a given day, varies according to the following rules: • If John cycles today, then the probability of him cycling tomorrow is 0.7 and the probability of him travelling by car is 0.2. • If John travels by car today, then the probability of him cycling tomorrow is 0.3 and the probability of him travelleing by train is 0.3. . Finally, if John travels by train today, then the probability of him cycling tomor- row is 0.2 and the probability of him travelling by car is 0.4. Assuming the above system can be described using a Markov Chain, answer the fol- lowing (a) Construct a transition diagram, clearly labelling the probabilities, to represent this situation. (5 marks) (b) Construct a transition matrix to represent this situation. (5 marks] (C) If John cycles today, what is the probability that he will travel by car in 4 days' time? (8 marks) (d) Determine the long-term probability for each scenario. [14 marks]