Question

A short-term insurance company receives five motor vehicle claims, on average per day. Assume that the daily claims follow a poisson process.

What is the probability that more than two motor vehicle claims received in any given day?

Answer 1

Given mean $\lambda=5$ ,

Probability that more than two motor vehicle claims received in any given day-

$=P(X>2)\\[9pt]=1-P(X\le 2)\\[9pt]=1-[P(X=0)+P(X=1)+P(X=2)]\\[9pt]=1-[\dfrac{e^{-\lambda}\lambda^0}{0!}+\dfrac{e^{-\lambda}\lambda^1}{1!}+\dfrac{e^{-\lambda}\lambda^2}{2!}]\\[9pt]=1-[\dfrac{e^{-5}5^0}{0!}+\dfrac{e^{-5}5^1}{1!}+\dfrac{e^{-5}5^2}{2!}]\\[9pt]=1-(0.006738+0.0336+0.08422)\\[9pt]=1-0.12456\\[9pt]=0.87543$