note that $\left( \Sigma^{\frac{1}{2}} \right)^{T}\Sigma^{\frac{1}{2}} = \Sigma$ %%visits: 2
Covariance matri := $\begin{pmatrix} \sigma_{11} & \sigma_{21} &
\ldots & \sigma_{1n} \\ \sigma_{21} & \ldots & &
\sigma_{2n} \\ \vdots \\ \end{pmatrix}$ where σij = Cov(Xi, Xj)
Properties of the Covariance matrix Symmetric: σij = σji
Positive definite Multivariate norma := mean vector and a
covariance matrix parameter. Covariance is linear. Multivariate vectors.
If X and Y are jointly normal then X is disjoint, independant to Y ⇔ cov(X, Y) = 0
A bivariate distribution is (X, Y) N(μ̂, Σ) and note that 2 independent and identically distributed normals make another normal.
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