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V1
Stat 230 Quiz #3 October 27, 2004
Version 1 Solution
1. Claims for a particular class of insurance arrive as a Poisson process at the rate of 3.6
per day (Monday to Friday).
(a) [2 marks] Find the probability that 4 claims arrive on a particular Monday.
Since we have a Poisson process, the number of claims on a given day is Poisson with
rate 3.6. Hence we have
Pr(
(
.
4
3 6
claims on Monday) =
3.6
4!
4
e

=
0.191)
(b) [4 marks] Suppose
X
is the number of days in a 5 day week with exactly 4 claims.
Explain, using the conditions for a Poisson process, what is the distribution of X?
The number of claims in any nonoverlapping days are independent. On any day we
can get 4 claims or not and the probability of 4 claims on any day is given by the
result in (a). Hence
X
is a binomial random variable with
n
=
5 and
p
e
=
3.6
4!
4

3 6
.
(c) [6 marks] Suppose that 17 claims arrive in one 5 day week. What is the probability
that there were exactly 4 claims on Monday?
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This note was uploaded on 10/21/2010 for the course STAT 230 taught by Professor Various during the Fall '06 term at Waterloo.
 Fall '06
 various
 Probability

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