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
Random real number percentile
Definition D2899
Random real number median
Formulation 0
Let $X \in \text{Random}(\mathbb{R})$ be a D3161: Random real number.
A D993: Real number $x \in \mathbb{R}$ is a median for $X$ if and only if
(1) \begin{equation} \mathbb{P}(X \leq x) \geq \frac{1}{2} \end{equation}
(2) \begin{equation} \mathbb{P}(X \geq x) \geq \frac{1}{2} \end{equation}
Results
Median need not be unique for a random real number