ThmDex – An index of mathematical definitions, results, and conjectures.
F11516
Formulation 1
Let $T \in \text{Exp}(\theta)$ be an D214: Exponential random positive real number.
Let $B \in \mathcal{B}(\mathbb{R})$ be a D5113: Standard real Borel set.
Then \begin{equation} \mathbb{P}(T \in B) = \int_B \theta e^{- \theta t} I_{[0, \infty)}(t) \, d t \end{equation}