Poisson Distribution

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space if these events occur with a known constant mean rate and independently of the time since the last event.

The Poisson distribution is often used to model the number of occurrences of events such as:

• The number of accidents in a given period of time
• The number of customers arriving at a store in a given hour
• The number of defects in a manufactured product

The Poisson distribution is defined by the following formula:

P(x) = (e^(−λ)*λ^(x))/x!

where:

• x is the number of events that occur
• λ is the mean rate of occurrence

The Poisson distribution is a versatile tool that can be used to model a wide variety of phenomena. It is a good choice for modeling events that occur randomly and independently.

Here are some of the benefits of using the Poisson distribution:

• It is a simple and elegant model.
• It is easy to estimate the parameters of the distribution.
• It can be used to make predictions about future events.
• It can be used to compare different events.

If you are looking for a model to describe a random and independent event, the Poisson distribution is a good choice.