V2
Stat 230 Quiz #3 Version 2 Solution
1. Claims for a particular class of insurance arrive as a Poisson process at the rate of 2.6
per day (Monday to Friday).
(a) [2 marks] Find the probability that 3 claims arrive on a particular Monday.
Since we have a Poisson process, the number of claims on a given day is Poisson with
rate 2.6. Hence we have
3
2.6
2.6
Pr(3claims on Monday)=
(
0.218)
3!
e

=
(b) [4 marks] Suppose
X
is the number of days in a 5 day week with exactly 3 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 3 claims or not and the probability of 3 claims on any day is given by the
result in (a). Hence
X
is a binomial random variable with
n
=
5 and
3
2.6
2.6
=
3!
p
e

(c) [6 marks] Suppose that 14 claims arrive in one week. What is the probability that
there were exactly 3 claims on Monday?
Let
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 Fall '06
 various
 Probability, Variance, Probability theory, Poisson process

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