The binomial distribution, in the limit of a large number of trials, is well approximated by a normal distribution with matching mean and variance. Proved first by Abraham de Moivre for fair coin flips and generalized by Pierre-Simon Laplace, it is the earliest known special case of the central limit theorem.
Facts
StatementThe theorem states that the binomial distribution can be approximated by the normal distribution as the number of trials grows large, a special case of the central limit theorem, with de Moivre proving the equal probability case and Laplace later extending it to any fixed success probability. 1 Proof YearDe Moivre's original result appeared in the second edition of The Doctrine of Chances in 1738. Pierre-Simon Laplace published the more general result in 1812. Classification
Statement Form Connections
Sources
1. De Moivre-Laplace Theorem (Wikipedia)
Wikimedia Foundationlead paragraph, first sentence
In probability theory, the de Moivre-Laplace theorem, which is a special case of the central limit theorem, states that the normal distribution may be used as an approximation to the binomial distribution under certain conditions.
history section, attribution sentence
The theorem appeared in the second edition of The Doctrine of Chances by Abraham de Moivre, published in 1738.
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