# Poisson Distribution

## Poisson Distribution Tutorial

##### Definition:

In statistics, poisson distribution is one of the discrete probability distribution. This distribution is used for calculating the possibilities for an event with the given average rate of value(λ). A poisson random variable(x) refers to the number of success in a poisson experiment.

#### Formula:

f(x) = eλx / x!
###### where,

λ is an average rate of value. x is a poisson random variable. e is the base of logarithm(e=2.718).

##### Example:

Consider, in an office 2 customers arrived today. Calculate the possibilities for exactly 3 customers to be arrived on tomorrow.

###### Step 1:

Find e. where, λ=2 and e=2.718 e = (2.718)-2 = 0.135.

###### Step 2:

Find λx. where, λ=2 and x=3. λx = 23 = 8.

###### Step 3:

Find f(x). f(x) = eλx / x! f(3) = (0.135)(8) / 3! = 0.18. Hence there are 18% possibilities for 3 customers to be arrived on tomorrow.

This tutorial will guide you to calculate the poisson distribution.