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.
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