Illustration of The Central Limit Theorem

Illustration Of The Central Limit Theorem

This article gives two concrete illustrations of the central limit theorem. Both involve the sum of independent and identically-distributed random variables and show how the probability distribution of the sum approaches the normal distribution as the number of terms in the sum increases.

The first illustration involves a continuous probability distribution, for which the random variables have a probability density function.

The second illustration, for which most of the computation can be done by hand, involves a discrete probability distribution, which is characterized by a probability mass function.

A free full-featured interactive simulation that allows the user to set up various distributions and adjust the sampling parameters is available through the External links section at the bottom of this page.

Read more about Illustration Of The Central Limit Theorem:  Illustration of The Continuous Case, Illustration of The Discrete Case

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