Answer to Question #341517 in Statistics and Probability for Lola

Question

QUESTION III

A short term insurance company receives three motor vehicle claims, on average, per day. Assume that

the daily claims follow a Poisson process.

Required:

a) What is the probability that at most two motor vehicle claims are received in any given day?

b) What is the probability that more than two motor vehicle claims are received in any given period

of two days?

Answer 1

Let $X=$ the number of motors received: $X\sim Po(\lambda t)$

a) Given $\lambda t=3(1)=3$

$$P(X\le2)=P(X=0)+P(X=1)+P(X=2)$$

$$=\dfrac{e^{-3}(3)^0}{0!}+\dfrac{e^{-3}(3)^1}{1!}+\dfrac{e^{-3}(3)^2}{2!}$$

$$=8.5e^{-3}=0.423190$$

b) Given $\lambda t=3(2)=6$

$$P(X>2)=1-P(X=0)-P(X=1)-P(X=2)$$

$$=1-\dfrac{e^{-6}(6)^0}{0!}-\dfrac{e^{-6}(6)^1}{1!}-\dfrac{e^{-6}(6)^2}{2!}$$

$$=1-25e^{-6}=0.938031$$