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}