Let X be a random variable, it is said to follow binomial distribution if it follows the following probability mass function. And it can have only non-negative values. The binomial distribution is a discrete probability distribution.

Binomial distribution is used to model problems, for instance, getting number of success after certain number of random experiments or trials.

**Example-**

**Problem-** If there are four coins which are tossed simultaneously, calculate the probability of getting at least two heads.

**Solution-**

Probability of getting head of a coin = 1/2

Probability of getting tail of a coin= 1/2

i.e

p=1/2 and q=1/2

probability of getting x heads in trials of 4 coins is

Therefore probability of getting at least two heads are

**Mean or Expectation of Binomial Distribution-**

**Mean or Expectation of Binomial Distribution-**

Expectation or mean of binomial distributed random variable X is

## Variance of binomial distributed random variable X is

**Python Code for Binomial Distribution**

**Python Code for Binomial Distribution**

**from scipy.stats import binom import numpy as np import matplotlib.pyplot as plt # Let lambda=np=5 x = np.arange(0,10) n=50 p=0.10 plt.plot(x, binom.pmf(x, n, p)) plt.savefig(“binom.png”)**

**Conclusion**

In this post, I have explained about binomial distribution. Hope you will understand and apply it.

**References**

- Fisz, M. and Bartoszyński, R., 2018.
*Probability theory and mathematical statistics*(Vol. 3). J. wiley. - Sahoo, P., Department of Mathematics University of Louisville Louisville, KY 40

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