ThmDex – An index of mathematical definitions, results, and conjectures.
Random unsigned basic number has zero correlation with the empty indicator
Formulation 0
Let $X \in \text{Random}[0, \infty]$ be a D5101: Random unsigned basic number.
Then \begin{equation} \mathbb{E}(X I_{\emptyset}) = 0 \end{equation}
Proofs
Proof 0
Let $X \in \text{Random}[0, \infty]$ be a D5101: Random unsigned basic number.
This result is a particular case of R5300: Unsigned basic integral over an empty set equals zero. $\square$