  # Poisson Distribution

## What is a Poisson Distribution?

A Poisson Distribution is a statistical distribution used to express the probability of a given number of events occurring within a fixed interval of time or space. Additionally, the events must occur independently of each other and with a known constant rate. For example, the average number of pennies thrown into a fountain per hour may follow a poisson distribution as the pennies all come from independent sources and arrive independently of each other.

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## How does a Poisson Distribution work?

A Poisson Distribution can be used if factors within the environment satisfy the requirements. Firstly, the number of times an event occurs must be a real number. Second, each event must occur independently of other events, and the average rate of the events is constant. Lastly, two events cannot occur simultaneously, and should the data infer so, the intervals should be broken into smaller sub-intervals. In essence, if two events occur in the same second, determine which came first using milliseconds.

### Examples of Poisson Distributions

A common example of data that would fit a Poisson distribution is the amount of mail one receives per day. It is possible to determine the average amount of mail one receives, and the individual pieces of mail are coming from independent sources. Additionally, the mail comes at a constant rate throughout the week. It is reasonable to assume the number of pieces of mail one receives each day would follow a Poisson distribution.

Another example could be the number of calls that a call center receives each hour. The calls each come independently of each other and from independent sources. Furthermore, the rate at which they come is constant (every hour per operating day). The average number of calls that a call center receives each day would likely follow a Poisson distribution.