Multivariate Normal distribution

$x$ is a $P\times 1$ random vector and has a multivariate normal distribution, denoted by $N(\mu,\sigma^2 \Sigma)$, if its density is given by:

$$\mathcal{N}(x;\mu,\sigma^2 \Sigma)= \frac{1}{(2\pi)^{P/2} \vert\s... ...ma\vert^{1/2}} exp\left(-\frac{1}{2\sigma^2}(x-\mu)^T\Sigma^{-1}(x-\mu) \right)$$ (23)

The multivariate normal distribution has mean$=\mu$ and covariance$=\sigma^2\Sigma$.