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

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

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

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

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

Then \begin{equation} \mathbb{E}[(X - \mathbb{E} X) (Y - \mathbb{E} Y)] = \mathbb{E} (X Y) - \mathbb{E} (X) \mathbb{E} (Y) \end{equation}

Let $X, Y \in \text{Random}(\mathbb{R})$ each be a D3161: Random real number such that

(i)	\begin{equation} \mathbb{E} |X|^2, \mathbb{E} |Y|^2 \in [0, \infty) \end{equation}

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