Multivariate Normal Distribution - Notation and Parametrization

Notation and Parametrization

The multivariate normal distribution of a k-dimensional random vector x = can be written in the following notation:

$\mathbf{x}\ \sim\ \mathcal{N}(\boldsymbol\mu,\, \boldsymbol\Sigma),$

or to make it explicitly known that X is k-dimensional,

$\mathbf{x}\ \sim\ \mathcal{N}_k(\boldsymbol\mu,\, \boldsymbol\Sigma).$

with k-dimensional mean vector

and k x k covariance matrix