ThmDex – An index of mathematical definitions, results, and conjectures.

Real calculus expression for distribution function of exponential random positive real number

Formulation 0

Let $T \in \text{Exp}(\theta)$ 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) = \left( 1 - e^{- \theta t} \right) I_{[0, \infty)} (t) \end{equation}

Formulation 1

Let $T \in \text{Exp}(\theta)$ 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) = \left( 1 - e^{- \theta t} \right) I_{t \in [0, \infty)} \end{equation}