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

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