$\rho$ (Coefficient of correlation between $X$ and $Y$)
-1.0
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
0
$E(X)$
$\text{Var}(X)$
$E(Y)$
$\text{Var}(Y)$
-4
-2
0
2
4
-4
-2
0
2
4
$Y$
$X$
$\begin{pmatrix} X \\ Y \end{pmatrix} \sim \mathcal{N} \left[\begin{pmatrix} 0 \\ 0 \end{pmatrix}, \begin{pmatrix} 1 & 0 \\ 0 & 1\end{pmatrix} \right]$
$E\left[ Y \vert X \right] = 0+0 \cdot \left ( X +0 \right)$