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- Conditional Mean and Variance

Conditional Variance

Discrete Random Vector

$σ_{x_{1} | x_{2}}^{2} = v a r (x_{1} | x_{2}) = E [(x_{1} - μ_{x_{1} | x_{2}})^{2} | x_{2}]$
Minus the Conditional Mean
$σ_{x_{1} | x_{2}}^{2} = v a r (x_{1} | x_{2}) = E [X_{1}^{2} | X_{2}] - (μ_{X_{1} | X_{2}})^{2}$

Continuous Random Vector

$σ_{x_{1} | x_{2}}^{2} = v a r (x_{1} | x_{2}) = E [X_{1}^{2} | X_{2}] - (μ_{X_{1} | X_{2}})^{2}$