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.
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}