Poisson distribution Facts for Kids

Typical Poisson distribution

In probability and statistics, Poisson distribution is a probability distribution. It is named after Siméon Denis Poisson, who discovered it in 1838. It measures the probability that a certain number of events occur within a certain period of time. The events need to be unrelated to each other. They also need to occur with a known average rate, represented by the symbol $\lambda$ (lambda).

More specifically, if a random variable $X$ follows Poisson distribution with rate $\lambda$ , then the probability of the different values of $X$ can be described as follows:

P(X=x)=\frac{e^{-\lambda} \lambda^x}{x!}

for

x = 0, 1, 2, \ldots

Examples of Poisson distribution include:

The numbers of cars that pass on a certain road in a certain time
The number of telephone calls a call center receives per minute
The number of light bulbs that burn out (fail) in a certain amount of time
The number of mutations in a given stretch of DNA after a certain amount of radiation
The number of errors that occur in a system
The number of Property & Casualty insurance claims experienced in a given period of time

For instance, an individual keeping track of the amount of mail they receive each day may notice that they receive an average number of 4 letters per day. If receiving any particular piece of mail does not affect the arrival times of future pieces of mail, i.e., if pieces of mail from a wide range of sources arrive independently of one another, then a reasonable assumption is that the number of pieces of mail received in a day obeys a Poisson distribution.

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Chewing gum on a sidewalk. The number of chewing gums on a single tile is approximately Poisson distributed.

Poisson distribution facts for kids

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