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Suppose that whether or not it rains today depends on previous weather conditions through the last...

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Statistics

Suppose that whether or not it rains today depends on previousweather conditions through the last two days. Specifically, supposethat if it has rained for the past two days, then it will raintomorrow with probability 0:7; if it rained today but notyesterday, then it will rain tomorrow with probability 0:5; if itrained yesterday but not today, then it will rain tomorrow withprobability 0:4; if it has not rained in the past two days, then itwill
rain tomorrow with probability 0:2. If we let the state attime n depend only on whether or not it is raining at time n,

Q1：The preceding would then represent a four-state Markovchain having a transition probability matrix P, and find P,plz?

Q2：Given that it rained on Monday and Tuesday, what is theprobability that it will rain on Thursday?

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