A D5291: Random real collection $X : J \to \text{Random}(\mathbb{R})$ is a weak white noise random real collection if and only if

(1)	\begin{equation} \forall \, j \in J : \mathbb{E} X_j \in \mathbb{R} \end{equation}
(2)	\begin{equation} \forall \, j \in J : \text{Var} X_j \in (0, \infty) \end{equation}
(3)	\begin{equation} \forall \, i, j \in J \left( i \neq j \quad \implies \quad \text{Cov}(X_i, X_j) = 0 \right) \end{equation}