# Poisson Probability Distribution

JoVE Core
Statistik
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JoVE Core Statistik
Poisson Probability Distribution

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The Poisson distribution is a type of discrete probability distribution which applies to event occurrences over a specified interval, such as time, volume, distance, or any similar unit.

Consider the data on daily car sales with a mean of three per day. In this case, the Poisson distribution can be used to predict the degree of spread around the mean value.

For instance, it can predict the probability of selling exactly 4 cars on a given day, using the formula for Poisson distribution. This probability value depends only on the mean and not on previous sales history.

Using the same formula, all other probabilities can be calculated and plotted for better visual representation.

The standard deviation for a Poisson distribution is given by the square root of the mean.

Unlike binomial distribution, the Poisson distribution is only affected by the mean and not by sample size or probability. Plus, the random variable in the Poisson distribution has no upper limit.

## Poisson Probability Distribution

A Poisson probability distribution is a discrete probability distribution. It gives the probability of a number of events occurring in a fixed interval of time or space if these events happen at a known average rate and independently of the time since the last event. For example, a book editor might be interested in the number of words spelled incorrectly in a particular book. It might be that, on average, there are five words spelled incorrectly in 100 pages. The interval is 100 pages.

The Poisson distribution may be used to approximate the binomial if the probability of success is "small" (such as 0.01) and the number of trials is "large" (such as 1,000).

This text is adapted from Openstax, Introductory Statistics, Section 4.6