The experiment is to run a Poisson process until time

**t**. The arrivals are shown as red dots on a timeline, and the number of arrivals**N**is recorded on each update. The density and moments of**N**are shown in blue in the distribution graph and are recorded in the distribution table. On each update, the empirical density and moments are shown in red in the distribution graph and the moments are recorded in the distribution table. The parameters of the experiment are the rate of the process**r**and the time**t**, which can be varied with scroll bars.## 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.

He published between 300 and 400 mathematical works in all. Despite this exceptionally large output, he worked on one topic at a time.

## Software/Applets used on this page

an applet from PSOL from UAH

## Glossary

### density

the ratio of the mass of an object to its volume

### event

any set of possible outcomes of a statistical experiment

### graph

A diagram showing a relationship between two variables.

The diagram shows a vertical y axis and a horizontal x axis.

The diagram shows a vertical y axis and a horizontal x axis.

### 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.

### work

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

## This question appears in the following syllabi:

Syllabus | Module | Section | Topic | Exam Year |
---|---|---|---|---|

AQA A-Level (UK - Pre-2017) | S2 | The Poisson Distribution | The shape of the distribution | - |

AQA AS Further Maths 2017 | Statistics | Poisson Distribution | Shape of Poisson Distribution | - |

AQA AS/A2 Further Maths 2017 | Statistics | Poisson Distribution | Shape of Poisson Distribution | - |

CCEA A-Level (NI) | S1 | The Poisson Distribution | The shape of the distribution | - |

CIE A-Level (UK) | S2 | The Poisson Distribution | The shape of the distribution | - |

Edexcel A-Level (UK - Pre-2017) | S2 | The Poisson Distribution | The shape of the distribution | - |

Edexcel AS Further Maths 2017 | Further Statistics 1 | Poisson Distributions | Shape of Poisson Distribution | - |

Edexcel AS/A2 Further Maths 2017 | Further Statistics 1 | Poisson Distributions | Shape of Poisson Distribution | - |

I.B. Higher Level | 7 | The Poisson Distribution | The shape of the distribution | - |

Methods (UK) | M15 | The Poisson Distribution | The shape of the distribution | - |

OCR A-Level (UK - Pre-2017) | S2 | The Poisson Distribution | The shape of the distribution | - |

OCR AS Further Maths 2017 | Statistics | Poisson Distribution | Shape of Poisson Distribution | - |

OCR MEI AS Further Maths 2017 | Statistics A | Poisson Distribution | Shape of Poisson Distribution | - |

OCR-MEI A-Level (UK - Pre-2017) | S2 | The Poisson Distribution | The shape of the distribution | - |

Universal (all site questions) | P | The Poisson Distribution | The shape of the distribution | - |

WJEC A-Level (Wales) | S1 | The Poisson Distribution | The shape of the distribution | - |