Question

 A short-term insurance company receives seven motor vehicle claims, on average, per day. Assume that the daily claims rate follows a Poisson process.

Calculate all the probabilities using the Poisson formula What is the probability that on a given day no more than five motor vehicle claims will be received?        

Answer 1

$P(X\le5)=P(X=0)+P(X=1)+P(X=2)+P(X=3)+P(X=4)+$

$+P(X=5)=e^{-7}(\frac{7^0}{0!}+\frac{7^1}{1!}+\frac{7^2}{2!}+\frac{7^3}{3!}+\frac{7^4}{4!}+\frac{7^5}{5!})=0.3007.$