# binomial distribution

(1.6 hours to learn)

## Summary

The binomial distribution describes the number of successes in a fixed number of independent trials, each with the same success probability. When the number of trials is large, the distribution is approximately bell-shaped.

## Context

This concept has the prerequisites:

## Goals

• Know the PMF of the binomial distribution
• Interpret the distribution in terms of i.i.d. Bernoulli random variables
• Describe the shape of the distribution
• Derive the expectation and variance of a binomial random variable

## -Free-

Mathematical Monk: Probability Primer (2011)
Online videos on probability theory.

## -Paid-

• The multinomial distribution is the analog of the binomial distribution where each event can take more than two values.
• The probability parameter can be estimated from data using maximum likelihood .
• The Poisson distribution is the limiting case as the number of trials goes to infinty and the success probability goes to zero.
• When the number of trials is large, the binomial distribution is well approximated by the Gaussian distribution. This follows from the Central Limit Theorem .