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If X \sim P_o(\lambda) \quad then P(X=x) = \displaystyle \frac{e^{-\lambda} \lambda^x}{x!}

## Summary/Background The Poisson distribution was discovered by Siméon-Denis Poisson (21 June 1781 – 25 April 1840) and published, together with his probability theory, in 1838 in his work Recherches sur la probabilite des jugements en matieres criminelles et matiere civile ("Research on the Probability of Judgments in Criminal and Civil Matters"). In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a fixed period of time if these events occur with a known average rate, and are independent of the time since the last event.
He published between 300 and 400 mathematical works in all. Despite this exceptionally large output, he worked on one topic at a time. You can get a better display of the maths by downloading special TeX fonts from jsMath. In the meantime, we will do the best we can with the fonts you have, but it may not be pretty and some equations may not be rendered correctly.

## Glossary

### event

any set of possible outcomes of a statistical experiment

### period

the horizontal length of one complete cycle

### poisson distribution

A distribution used to estimate probabilities of random events which have a small probability of occuring, for example volcanic eruptions, accident rates.

### union

The union of two sets A and B is the set containing all the elements of A and B.

### work

Equal to F x s, where F is the force in Newtons and s is the distance travelled and is measured in Joules.

Full Glossary List

## This question appears in the following syllabi:

SyllabusModuleSectionTopicExam Year
AQA A-Level (UK - Pre-2017)S2The Poisson DistributionProbabilities-
AQA AS Further Maths 2017StatisticsPoisson DistributionPoisson Probabilities-
AQA AS/A2 Further Maths 2017StatisticsPoisson DistributionPoisson Probabilities-
CBSE XII (India)ProbabilityProbabilityRepeated independent (Bernoulli) trials and binomial distribution-
CCEA A-Level (NI)S1The Poisson DistributionProbabilities-
CIE A-Level (UK)S2The Poisson DistributionProbabilities-
Edexcel A-Level (UK - Pre-2017)S2The Poisson DistributionProbabilities-
Edexcel AS Further Maths 2017Further Statistics 1Poisson DistributionsPoisson Probabilities-
Edexcel AS/A2 Further Maths 2017Further Statistics 1Poisson DistributionsPoisson Probabilities-
I.B. Higher Level7The Poisson DistributionProbabilities-
Methods (UK)M15The Poisson DistributionProbabilities-
OCR A-Level (UK - Pre-2017)S2The Poisson DistributionProbabilities-
OCR AS Further Maths 2017StatisticsPoisson DistributionPoisson Probabilities-
OCR MEI AS Further Maths 2017Statistics APoisson DistributionPoisson Probabilities-
OCR-MEI A-Level (UK - Pre-2017)S2The Poisson DistributionProbabilities-
Universal (all site questions)PThe Poisson DistributionProbabilities-
WJEC A-Level (Wales)S1The Poisson DistributionProbabilities-