Central Limit Theorem

(1.4 hours to learn)


The Central Limit Theorem states that the sum of a large number of independent, identically distributed random variables is approximately Gaussian. It can be used to approximate the probability that a sum of independent random variables lies within some range, even if the distributions are otherwise hard to work with. This theorem is one of the reasons that Gaussian distributions are so ubiquitous in statistics and probabilistic modeling.


This concept has the prerequisites:


  • Know the statement of the central limit theorem
  • Be able to use it to estimate the distribution of a sum of i.i.d. random variables
  • Prove the theorem

Core resources (read/watch one of the following)


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


Mathematical Monk: Probability Primer (2011)
Stats.Stackexchange Question: What intuitive explanation is there for the central limit theorem?
Location: answer from user 'whuber'


See also