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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 Spring '11
 CharlesDann
 Probability theory, Exponential distribution, insurance policy, Geometric distribution, Snow Removal, major snowstorms

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