ThmDex – An index of mathematical definitions, results, and conjectures.
F11866
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}