# Why is a Poisson distribution important?

Dec 16, 2017

See below.

#### Explanation:

The Poisson probability distribution often provides a good model for the probability distribution of the number of $Y$ "rare" events that occur in space, time, volume, or any other dimension.

Examples include car/industrial accidents, telephone calls handled by a switchboard in a time interval, number of radioactive particles that decay in a particular time period, etc.

One particular use of the Poisson distribution is in queuing theory. In essence, the Poisson distribution can be used to model customers arriving in a queue, such as when checking out items at a store. It can be determined using the distribution what the most efficient way of organizing this queue is.

For example, you've probably been to a store which organizes shoppers ready to check out by having them all stand in one line, which then leads to multiple registers. When one register is free, the next person in line may check out (I see this often at banks). This has proven to be the most efficient method (as far as I am aware). This is opposed to those businesses which have multiple registers, each with their own separate line, which has proven to be rather inefficient using the Poisson distribution as a model.