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 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