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A Note On The Asymptotic Convergence of Bernoulli Distribution

Abstract

This paper presents concepts of Bernoulli distribution, and how it can be used as an approximation of Binomial, Poisson and Gaussian distributions with different approach from earlier existing literatures. Due to discrete nature of the random variable X, a more appropriate method of Principle of Mathematical Induction (PMI) is used as an alternative approach to limiting behavior of binomial random variable. The study proved de'Moivres Laplace theorem (convergence of binomial distribution to Gaussian distribution) to all values of p such that p p ≠ 0 and p ≠ 1 using a direct approach which opposes the popular and most widely used indirect method of moment generating function.

Adeniran Adefemi T, Ojo J. F. and Olilima J. O

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