Question

A short term insurance company receives three vehicle claims related calls, on average, per hour. Assume that the daily claims follow a poisson process. how many claims related calls does company expect to receive in a period of three hours?

Answer 1

Let $X=$ the number of claims related calls: $X\sim Po(\lambda t)$

$$\lambda t=3 h^{-1}(3\ h)=9$$

If$X$ has a Poisson distribution with parameter $\mu,$

$$E(X)=V(X)=\mu$$

Therefore company expects to receive $9$ claims related calls in a period of three hours.