▾ Set of symbols
▾ Alphabet
▾ Deduction system
▾ Theory
▾ Zermelo-Fraenkel set theory
▾ Set
▾ Subset
▾ Power set
▾ Hyperpower set sequence
▾ Hyperpower set
▾ Hypersubset
▾ Subset algebra
▾ Subset structure
▾ Measurable space
▾ Measure space
▾ Pushforward measure
▾ Distribution measure
▾ Probability distribution measure
▾ Probability distribution function
Exponential probability distribution function
Formulation 0
The exponential probability distribution function with parameter $\theta > 0$ is the D4367: Unsigned real function \begin{equation} \mathbb{R} \to [0, 1], \quad x \mapsto (1 - e^{- \theta x}) I_{x \geq 0} \end{equation}
Formulation 1
The exponential probability distribution function with parameter $\theta > 0$ is the D4367: Unsigned real function \begin{equation} \mathbb{R} \to [0, 1], \quad x \mapsto \begin{cases} 1 - e^{- \theta x}, \quad & x \in [0, \infty) \\ 0, \quad & x \in (-\infty, 0) \end{cases} \end{equation}