Multivariate Gaussian Distribution

Multivariate Gaussian Distribution

Random variable x follows normal distribution with mean μ and variance σ2, 
denoted as x ~ G(μ, σ2). The density function is

is quadratic function of random variable x, 
and is a constant that does not depend on x. 
The density function could be rewritten as

Consider the joint distribution with a vector-valued random variables X=(x1,…xn)T. 
The density function of multivariate Gaussian distribution (MVG) with mean vector μ and variance-covariance matrix Σ.

Further, Consider Y=AX+C if X ~ MVG(μ,Σ), and A, C are constant matrix.