Question

A short-term insurance company receives, in each working day, three motor vehicle claims. Assume that the daily claims rate follow a Poisson process. How likely is it that either eight or nine motor vehicle claims will be received in two working days? Express your answer to 4 decimal places.

Answer 1

Let $X=$ the number of received motor vehicle claims: $X\sim Po(\lambda t).$  

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

$$P(X=8\ or X=9)=\dfrac{e^{-6}\cdot6^8}{8!}+\dfrac{e^{-6}\cdot6^9}{9!}$$

$$\approx0.1721$$