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

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 $$X \overset{d}{=} \frac{1}{\theta} T$$
Children
 ▶ Erlang random positive real number
Results
 ▶ Expectation of exponential random positive real number ▶ Independent minimums preserve exponential distribution ▶ Probability density function for standard exponential random positive real number ▶ Probability to win an I.I.D. exponential race