ThmDex – An index of mathematical definitions, results, and conjectures.

ThmDex – An index of mathematical definitions, results, and conjectures.

Result R5301 on D5103: Unsigned basic expectation

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. $\square$