A random variable X is said to follow Poisson distribution, if it follows the following probability distribution function.

Poisson distribution is a discrete probability distribution.

It models the following types of problems

- Find out number of new born babies in a city in certain time duration.
- Find out defective materials in manufactured by a company.
- Number of printing errors in a page.

## Mean of Poisson Distribution’s Random Variable X-

Mean of Poisson distribution’s random variable X is derived below

## Numerical Problem Poisson Distribution

**Question-**

A company manufactures 10 materials in a day in which 10% are defective, calculate the probability that at least two materials will not be defective.

**Answer-**

** **Here n=10 p=10%=1/10

Then λ=n p= 10 * (1/10)=1

Then we have to calculate

probability that at least two materials will not be defective.

P(X=0)+P(X=1)+P(X=2) = λ^{} e^{-1 }/0! + λ^{1} e^{-1}/1! + λ^{2} e^{-1}/2!

Calculate it yourself

**Variance of Poisson Distribution Random Variable X-**

**Variance of Poisson Distribution Random Variable X-**

Variance of Poisson distribution’s random variable X is derived below

## Python Code for Poisson Distribution

**from scipy.stats import poisson**

**import numpy as np **

**import matplotlib.pyplot as plt**

**x= np.arange(1000,2000,0.5)**

**plt.plot(x, poisson.pmf(x,1500))**

**plt.savefig(“poisson.jpg”)**

## Output

When mean p=0.50 and mean=1500

When mean p=0.50 and mean=1000

## Conclusion

To sum up, in this post I have explained about Poisson distribution and its applicability is domains. Hope you will understand and apply.

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