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Homework 1 (due Jan. 25)
1. Consider the 1700 ship insurance business situation discussed in class.
The probability of any ship being lost at sea is 0.015, independent of other
ships. Suppose that the goal of every insurance “company” is to have the
probability of a ﬁnancial loss not exceeding 0.05. A small company insures
1000 ships and a large company insures 2000 ships. Can the large company
aﬀord a smaller premium while still achieving the goal of less than 0.05
ﬁnancial loss probability? How much smaller can the premium be? The
payoﬀ in case of a loss is 100,000 for any ship.
2. A lifetime of a light bulb is normally distributed with the mean of
10000 hours and standard deviation of 1000 hours. There are 100 such bulbs
in the building (installed at the same time).
a) What is the probability that any given bulb lasts more than 12000
hours?
b) What is the probability that any given bulb burns out before 9000
hours?
c) What is the probability that we would have to replace at least one bulb
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 Spring '08
 Perevalov

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