What is possion distribution and when to use it?

The Poisson distribution is a 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 can be used in various scenarios such as:

1. Modeling the number of times an event occurs in an interval of time or space. For example, the number of phone calls received by a call center per hour or the number of decay events per second from a radioactive source.

2. Estimating the probability of a given number of events in a fixed interval of time or space. For example, the probability of a certain number of users visiting a website in a given period.

3. Predicting the number of events in the future given the historical data. For example, predicting the number of accidents in a city given the past data.

The key assumptions for using the Poisson distribution are:

1. The events are independent of each other. The occurrence of one event does not affect the probability of the occurrence of another event.

2. The average rate (lambda) at which events occur is constant. It cannot be higher in some intervals and lower in other intervals.

3. Two events cannot occur at exactly the same instant.

4. The actual number of events in an interval can range from zero to infinity.