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
▼ Probability space
▼ Filtered probability space
▼ Random time
▼ Stopping time
▼ Negative binomial random natural number
▼ Geometric random positive integer
▼ Standard exponential random positive real number
Definition D214
Exponential random positive real number
Formulation 0
Let $T \in \text{Exp}(1)$ be a D4000: Standard exponential random positive real number.
A D3161: Random real number $X \in \text{Random}(0, \infty)$ is an exponential random positive real number with parameter $\theta \in (0, \infty)$ if and only if \begin{equation} X \overset{d}{=} \frac{1}{\theta} T \end{equation}
Children
▶ D4862: Erlang random positive real number
Results
▶ R2239: Expectation of exponential random positive real number
▶ R4794: Independent minimums preserve exponential distribution
▶ R4901: Probability density function for standard exponential random positive real number
▶ R5276: Probability to win an I.I.D. exponential race