Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a D1159: Probability space such that

(i)	$Z : \Omega \to \Xi$ is a D202: Random variable on $P$
(ii)	$X, Y : \Omega \to \mathbb{R}$ are each a D3161: Random real number on $P$
(iii)	\begin{equation} \mathbb{E} |X|^2, \mathbb{E} |Y|^2 < \infty \end{equation}

Then \begin{equation} \text{Cov}(X, Y \mid Z) = \mathbb{E}(X Y \mid Z) + \mathbb{E}(X \mid Z) \mathbb{E}(Y \mid Z) \end{equation}