The variance of Standard Normal Distribution represented by ##sigma^2## is equal to unity.

##sigma^2=1##

A Standard Normal Distribution is a normal distribution with zero mean (mu=0) and unit variance (sigma^2=1), given by the probability density function and distribution function

##P(x) = 1/(sqrt(2pi))e^(-x^2/2)##

##D(x) = 1/2[erf(x/(sqrt(2)))+1##

over the domain x in ##(-infty,infty)##

It has mean, variance, skewness, and kurtosis excess given by

##mu = 0##

##sigma^2 = 1##

##gamma_1 = 0##

##gamma_2 = 0##