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Fundamental Generation Systems
book

Fundamental Generation Systems

by Alain Cardon, Abdelkhalak El Hami
August 2023
Intermediate to advanced content levelIntermediate to advanced
224 pages
5h 12m
English
Wiley-ISTE
Content preview from Fundamental Generation Systems

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)

equation

We take the limit of this equation, knowing that:

equation

We can therefore show that:

equation
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Publisher Resources

ISBN: 9781786308733Purchase Link