1) Describe the problem using a system of difference equations. 2) Assume today is sunny, compute the distribution of the weather two days later (i.e., the probability of sunny, cloudy, or rainy two days later). 3) Give the general solution for this dynamic system. 4) Find the long-run distribution (i.e., the steady state) of weather for July date
Suppose that the weather in Ann Arbor in July can be characterized as sunny, rainy, or
cloudy (with no rain). By looking up back issues of the Ann Arbor News, we estimate that if it is
sunny on a July day, it is equally likely to be sunny or cloudy on the next day, but it won’t rain. If a
July day is cloudy, there is a 50 percent chance that it will rain on the next day, a 25 percent chance
that it will be sunny, and a 25 percent chance that it will remain cloudy without rain. If it rains on a
July day, it won’t be sunny the next day, and there is a 50-50 chance of continued rain.
1) Describe the problem using a system of difference equations.
2) Assume today is sunny, compute the distribution of the weather two days later (i.e., the probability of
sunny, cloudy, or rainy two days later).
3) Give the general solution for this dynamic system.
4) Find the long-run distribution (i.e., the steady state) of weather for July dates.
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