#precision-matrix

Question 1: Single choice

mediumAI-checkedProbabilistic & Graphical Models

For $p(\mathbf{x}) \propto \exp\left(-\tfrac{1}{2}\mathbf{x}^\top A \mathbf{x} - \mathbf{b}^\top \mathbf{x}\right)$ with $A$ symmetric (for real $\mathbf{x}$ , a Gaussian with precision matrix $A$ ), what does an off-diagonal entry $a_{ij} = 0$ imply?

$x_i \perp x_j$ when the other variables are not observed1
$x_i$ and $x_j$ are both independent of all other variables2
Nothing, unless the diagonal entries $a_{ii}$ and $a_{jj}$ are zero as well3
$x_i \perp x_j$ given all the other variables4

Timed test