# Poisson distribution.

• July 6th 2011, 02:00 PM
SLJSWW
Poisson distribution.
An insurance company receives on average 3 claims per month from a certain town.Assuming that the number of claims follows a Poisson distribution, find the probability
a) it receives less than 3 claims in a given month;
b) it receives more than 2 more in a given three month period

(Doh)pls help me solve...
• July 6th 2011, 02:47 PM
pickslides
Re: Help solve this probability question
Quote:

Originally Posted by SLJSWW
a) it receives less than 3 claims in a given month;

Make $\displaystyle \lambda = 3$ and find $\displaystyle P(x<3) = P(x=0)+P(x=1)+P(x=2)$

where $\displaystyle P(x=k) = \frac{\lambda^k\times e^{-\lambda}}{k!}$

Quote:

Originally Posted by SLJSWW

b) it receives more than 2 more in a given three month period

for a 3 month period make $\displaystyle \lambda = 3\times 3$ and find $\displaystyle P(x>2) = 1-P(x\leq 2)$

where $\displaystyle P(x=k) = \frac{\lambda^k\times e^{-\lambda}}{k!}$