Homework Assignment 4: (1) An insurance policy is written to cover a loss X, where X has a uniform distribution on [0, 1000]. At what level must a deductible be set in order for the expected payment to be 25% of what it would be with no deductible? (Ans 500) (2) Chapel Hill’s Public Works Department has estimated that the cost of snow removal after a major snowstorm is $100,000. Historical information suggests that the number of major snowstorms in a winter season follows a geometric distribution for which the probability of no major snowstorms in a season is 40%. The town purchases an insurance policy that pays nothing if the number of major snowstorms in a season is one or less, but the insurance pays 50% of ALL seasonal snow removal costs for major snowstorms if there are two or more major snowstorms. Find the expected payment to Chapel Hill under this policy during one season. (Ans 63,000) (3) Express trains arrive at a station at a Poisson rate of 5 per hour. Local trains arrive at a Poisson rate of 15 per hour. The type of each train is independent of
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