Let $T \in \mathsf{Exp}(\theta)$ be an D214: Exponential random positive real number.
Let $t \in \mathbb{R}$ be a D993: Real number.

Then \begin{equation} \mathbb{P}(T \leq t) = (1 - e^{- \theta t}) I_{t \geq 0} \end{equation}

Let $T \in \mathsf{Exp}(\theta)$ be an D214: Exponential random positive real number.
Let $t \in \mathbb{R}$ be a D993: Real number.

Then \begin{equation} \mathbb{P}(T \leq t) = \begin{cases} 1 - e^{- t \theta}, \quad & t \geq 0 \\ 0, \quad & t < 0 \end{cases} \end{equation}