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19.03.2020 • 
Mathematics

In a good weather year the number of storms is Poisson distributed with mean 1; in a bad year it is Poisson distributed with mean 3. Suppose that any year’s weather conditions depend on past years only through the previous year’s condition. Suppose that a good year is equally likely to be followed by either ESI 4313- Spring 20 a good or a bad year, and that a bad year is twice as likely to be followed by a bad year as by a good year. Suppose that last year—call it year 0—was a good year. a. Find the expected total number of storms in the next two years (that is, in years 1 and 2). b. Find the probability there are no storms in year 3. c. Find the long-run average number of storms per year.

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