Poisson Distribution in Statistics

Mean of Poisson Distribution Variable X

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.

Poisson Distribution PDF

Mean of Poisson Distribution’s Random Variable X-

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

Mean of Poisson Distribution Variable X

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!    + λ1 e-1/1!    +  λ2 e-1/2!

Calculate it yourself

 

Variance of Poisson Distribution Random Variable X-

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

Variance of Poisson Random Variable X

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

Python Code for Poisson Distribution

When mean p=0.50 and mean=1000

Poisson Distribution Plot

Conclusion

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

References

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1 Comment on "Poisson Distribution in Statistics"

  1. very interesting course .I need how to analyze data by spss soft ware

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