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23. 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 depends on past years only through the previous year's con- dition. Suppose that a good year is equally likely to be followed by either 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 yearcall it year 0was 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