Bernoulli Distribution in Probability and Statistics

Bernoulli Distribution
Data Science and A.I. Lecture Series
By Bindeshwar Singh Kushwaha | PostNetwork Academy
Introduction to Bernoulli Distribution

A Bernoulli trial is an experiment with only two possible outcomes: Success (1) and Failure (0).

If p is the probability of success, then q = 1 – p is the probability of failure.

A random variable X following a Bernoulli distribution takes values:

Properties of Bernoulli Distribution
The expectation (mean) of a Bernoulli distributed variable is:

The variance of a Bernoulli variable is:

The moments about the origin are given by:

If X₁, X₂, …, Xₙ are independent Bernoulli variables with the same p, their sum follows a Binomial distribution.
Example: Bernoulli Distribution

Suppose a coin is flipped, where heads is considered a success (p = 0.4) and tails a failure (q = 0.6).

The expected value is:

The variance is:

If we repeat this experiment multiple times, the sum follows a Binomial distribution.

Video

PDF

Bernoulli Distribution

 

Reach PostNetwork Academy
Website: www.postnetwork.co
YouTube Channel: www.youtube.com/@postnetworkacademy
Facebook Page: www.facebook.com/postnetworkacademy
LinkedIn Page: www.linkedin.com/company/postnetworkacademy
Thank You!

©Postnetwork-All rights reserved.