Suppose that whether or not it rains today depends on previous weather condition

Question

Suppose that whether or not it rains today depends on previous weather conditions through the last three days. Show how this system may be analyzed by using a Markov Chain. How many states are needed?

Suppose that if it has rained for the past three days, then it will rain today with probability 0.8; if it did not rain for any of the past three days, then it will rain today with probability 0.2; and in any other case the weather today will, with probability 0.6, be the same as the weather as yesterday. Determine P for this Markov Chain.

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