binomial distribution

(1.6 hours to learn)


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.


This concept has the prerequisites:


  • 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

Core resources (read/watch one of the following)


Khan Academy: Probability and Statistics


Supplemental resources (the following are optional, but you may find them useful)



See also

  • 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 .