A univariate Gaussian or normal distributions can be completely determined by its mean and variance. Gaussian distributions can be applied to a large numbers of problems because of the central limit theorem (CLT). The CLT posits that when a large number of independent and identically distributed ((i. i.d.) random variables are added, the cumulative distribution function (cdf) of their sum is approximated by the cdf of a normal distribution. Recall the probability density function of the univariate Gaussian with mean μ and variance σ2 , N(μ,σ2) : fX(x)=12πσ2−−−−√e−(x−μ)2/(2σ2).