Derivation of Gaussian Probability Distribution: A New Approach

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.

A Static Area Coverage Algorithm for Heterogeneous AUV Group Based on Biological Competition Mechanism

“…For any location r in a task region, assuming that there are m suspicious locations in the area. Target occurrence probability utilized by Gaussian probability function ( Adeniran et al, 2020 ; Fritz, 2020 ) can be expressed as where r i represents the location where the target is most likely to appear, which is mainly judged according to environmental features and prior knowledge. And we use random value in this work.…”

Mangat Randomized Response Group Testing Theory

“…When noise/disturbance arises due to sensitive nature of the survey question(s), randomised response theory invented by [1] gives a setting to construct techniques where these problems become well posed. To obtain estimator of specific quality (say, efficiency) and computational advantage (ease of mathematical workloads), measurement *Corresponding author: E-mail: at.adeniran@ui.edu.ng; noise is often assumed to follow Gaussian distribution in a wide range of applications [2]. The conventional method of data collection usually employed in ordinary statistical surveys, may suffer a surprising failure when applied on noisy data without choosing appropriate values for parameters to minimize the noise because obtaining truthful responses is challenging in all types of surveys, particularly, when sensitive subject matters are being investigated.…”