Derivation of Gaussian Probability Distribution: A New Approach

A T Adeniran ,O Faweya ,Temitope Olu Ogunlade ,Kayode Balogun

doi:10.4236/am.2020.116031

Abstract

The famous de Moivre’s Laplace limit theorem proved the probability density function of Gaussian distribution from binomial probability mass function under specified conditions. De Moivre’s Laplace approach is cumbersome as it relies heavily on many lemmas and theorems. This paper invented an alternative and less rigorous method of deriving Gaussian distribution from basic random experiment conditional on some assumptions.

Highlights

A well celebrated, fundamental probability distribution for the class of continuous functions is the classical Gaussian distribution named after the German
The well-known method of deriving this distribution first appeared in the second edition of the Doctrine of Chances by Abraham de Moivre published in 1738 ([1] [2] [3] [4] [5])
Suppose a random experiment of throwing needle or any other dart related objects at the origin of the cartesian plane is performed with the aim of hitting the centre

Summary

Introduction

A well celebrated, fundamental probability distribution for the class of continuous functions is the classical Gaussian distribution named after the German. 2πσ 2 is called the normal probability density function of a random variable X with parameters μ and σ. Both in theories and applications, without element of equivocation, the Gaussian distribution function is the most essential and widely referencing distribu-. The well-known method of deriving this distribution first appeared in the second edition of the Doctrine of Chances by Abraham de Moivre (de Moivre’s Laplace limit theorem) published in 1738 ([1] [2] [3] [4] [5]). We attempt to find an answer to the question: is there any alternative procedure to the derivation of Gaussian probability density function apart from de Moivre’s Laplace limit theorem approach which relies heavily on many. Lemmas and Theorems (Stirling approximation formula, Maclaurin series expansion etc.), as evidenced by the work of [8] and [9]?

Existing Technique

The Proposed Technique

Conclusion