Appendix 3Poisson Distribution
The Poisson distribution is generally used to assess risks in industry. It takes problems in time or space into account. If we wanted to solve this kind of problem with the Bernoulli distribution, we would have to decompose the time or space interval into very small parts, given that it only takes the occurrence or absence of an event into account. Let us suppose that the average occurrence of a tornado in a certain location is v times per year, where during a period of t years, a tornado will occur on average v × t times. If the period of time is divided by n intervals, the probability of a tornado occurring will be (v × t)/n. If we take x occurrences during a period of time t in a Bernoulli sequence when n tends to infinity, then we obtain the Poisson distribution, which can be expressed as follows:
P(x occurences in t)

We take the limit of this equation, knowing that:

We can therefore show that:
