Suppose that whether it rains or not depends on previous weather conditions through the last three days. Suppose that if it has rained for the past three days, then it will rain today with probability 0.7; if it did not rain for any of the past three days, then it will rain with probability 0.3; and in any other case the weather today will, with probability 0.6, be the same as the weather yesterday. a) Show how this system may be analyzed by defining an appropriate Markov chain. How many states are needed? b) Determine the one step transition probability matrix $P$ for this Markov chain.
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Since the weather depends on the last three days, we can represent the states as a sequence of three binary values, where 1 represents rain and 0 represents no rain. There are 2^3 = 8 possible states: Show more…
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