Statistics & Probability

A normal distribution in a variate with mean and variance is a statistic distribution with probability density function (1) on the domain . While statisticians and mathematicians uniformly use the term "normal distribution" for this distribution, physicists sometimes call it a Gaussian distribution and, because of its curved flaring shape, social scientists refer to it as the "bell curve." Feller (1968) uses the symbol for in the above equation, but then switches to in Feller (1971). de Moivre developed the normal distribution as an approximation to the binomial distribution , and it was subsequently used by Laplace in 1783 to study measurement errors and by Gauss in 1809 in the analysis of astronomical data (Havil 2003, p. 157). The normal distribution is implemented in Mathematica as NormalDistribution [ mu , sigma ]. The so-called " standard normal distribution " is given by taking and in a general normal distrib