ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Function
Real collection function
Euclidean real function
Real function
Rational function
Integer function
Natural number function
Boolean function
Indicator function
Definition D2796
Indicator random boolean number
Results
Expectation of an indicator random boolean number
Moments of an indicator random boolean number
Remarks
Remark 0 (Distribution of an indicator random number)
Let $P = (\Omega, \mathcal{F}, \mathbb{P})$ be a [[[d,1159]]]. If $I_E$ is an [[[d,2796]]] on $P$ for $E \in \mathcal{F}$, then the distribution of $I_E$ is immediately given by $\mathbb{P}(I_E = 1) = \mathbb{P}(E)$ and $\mathbb{P}(I_E = 0) = \mathbb{P}(\Omega \setminus E)$.