In an article published in the journal Science, Gray (1990) contrasts various aspects of Atlantic hurricanes occurring in drought versus wet years in sub-Saharan Africa. During the 18-year drought period 1970–1987, only one strong hurricane (intensity 3 or higher) made landfall on the east coast of the United States, but 13 such storms hit the eastern United States during the 23-year wet period 1947–1969.
a. Assume that the number of hurricanes making landfall in the eastern United States follows a Poisson distribution whose characteristics depend on African rainfall. Fit two Poisson distributions to Gray’s data (one conditional on drought, and one conditional on a wet year, in West Africa).
b. Compute the probability that at least one strong hurricane will hit the eastern United States, given a dry year in West Africa.
c. Compute the probability that at least one strong hurricane will hit the eastern United States, given a wet year in West Africa.
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