A Brief of Gaussian Distribution Gaussian distribution, also known as normal distribution, is the most popular continuous probability distribution.
In monovariate case, x∈(−∞,∞), parameters of the Gaussian distribution are average μ∈(−∞,∞)and variance σ2>0. The probability function is defined as follows
p(x|μ,σ2)=12πσ2−−−−√exp{−(x−μ)22σ2} E[x]=μ var[x]=σ2In multivariate case, consider the d-dimension vector x, the average μ is a d-dimension vector, too. However, the covariance in this case becomes a positive definite matrix Σ of d×d dimension.
p(x|μ,Σ)=1(2π)ddet(Σ)−−−−−−−−−−√exp{−12(x−μ)TΣ−1(x−μ)} E[x]=μ cov[x]=Σ