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Title: A DeMoivre-Laplace theorem of all orders of regularity
Authors: van den Berg, Imme
Keywords: Binomial distribution
DeMoivre-Laplace Theorem
Pascal Triangle
Gaussian distribution
difference quotients
discrete heat equation
nonstandard analysis
Issue Date: 2007
Publisher: Shaker Publishing, Maastricht/Aachen
Abstract: The DeMoivre-Laplace Theorem states that the binomial probability distribution B(N; 1/2) tends for N to infinity to the Gaussian distribution. We extend this theorem to the difference quotients of the family of the binomial distributions with varying N, showing that they converge to the corresponding differential quotients of the time-dependent Gaussian distribution. The convergence holds for difference quotients of all order.
Type: article
Appears in Collections:MAT - Artigos em Livros de Actas/Proceedings

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