ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Subset
Power set
Hyperpower set sequence
Hyperpower set
Hypersubset
Subset algebra
Subset structure
Measurable space
Measure space
Pushforward measure
Distribution measure
Probability distribution measure
Probability distribution function
Definition D2898
Random real number percentile
Formulation 2
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number.
A D993: Real number $x \in \mathbb{R}$ is a percentile for $X$ with respect to $p \in [0, 1]$ if and only if
(1) \begin{equation} \mathbb{P}(X \leq x) \geq p \end{equation}
(2) \begin{equation} \mathbb{P}(X \geq x) \geq 1 - p \end{equation}
Children
D2899: Random real number median