(i) | $X : \Omega \to [0, \infty]$ is a D5101: Random unsigned basic number on $P$ |

**expectation**of $X$ on $P$ is the D1699: Basic number \begin{equation} \mathbb{E}_{\mathbb{P}} X : = \int_{\Omega} X \, d \mathbb{P} \end{equation}

Definition D5103

Unsigned basic expectation

Formulation 0

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

The **expectation** of $X$ on $P$ is the D1699: Basic number
\begin{equation}
\mathbb{E}_{\mathbb{P}} X
: = \int_{\Omega} X \, d \mathbb{P}
\end{equation}

(i) | $X : \Omega \to [0, \infty]$ is a D5101: Random unsigned basic number on $P$ |

Children

▶ | Basic expectation |

Results

▶ | Probabilistic Tonelli's theorem |

▶ | Random unsigned basic number has zero correlation with the empty indicator |

▶ | Unsigned basic expectation zero iff random number almost surely zero |