ThmDex – An index of mathematical definitions, results, and conjectures.
F11227
Formulation 0
Let $T_1 \in \text{Exp}(\theta_1), \dots, T_N \in \text{Exp}(\theta_N)$ each be an D214: Exponential random positive real number such that
(i) $T_1, \dots, T_N$ is an D2713: Independent random collection
Then \begin{equation} \min(T_1, \ldots, T_N) \overset{d}{=} \text{Exp} \left( \sum_{n = 1}^N \theta_n \right) \end{equation}