Let $a, b \in \mathbb{R}$ each be a D993: Real number such that
| (i) | $a \leq b$ |
| (ii) | $[a, b] \subset \mathbb{R}$ is the D544: Closed real interval from $a$ to $b$ |
| (iii) | $X \in \text{Random}[a, b]$ is a D3161: Random real number |
Then
| (1) | \begin{equation} \mathbb{E} X = a \quad \implies \quad \mathbb{P}(X = a) = 1 \end{equation} |
| (2) | \begin{equation} \mathbb{E} X = b \quad \implies \quad \mathbb{P}(X = b) = 1 \end{equation} |