##### Poisson Distribution with Example

A random variable Y is said to be Poisson random variable if Y takes value 0,1,2,3... with λ as a parameter.

A Poisson random variable is used to approximate a binomial if the value of n is large and p is very small.

and λ = np

Example:-

1. The no. of an accident occurring on a highway each day is poisson random variable with parameter 3.

What is the probability that no accident occurred?

Solution:

They are clearly saying " no accident " which means i=0

So using the above formula :

p(i=0) =  (e-3 (3)) / 0 !

= e-3  or

1/ e3

remember  0! =1