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

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Result R5251 on D3838: Gamma random positive real number
Subresult of R5243: Finite sum of uncorrelated identically distributed exponential random positive real numbers is a gamma random random positive real number

Exponential random positive real number is a gamma random positive real number

Formulation 0

Let

$T \in \text{Exponential}(\theta)$ be an D214: Exponential random positive real number.

Then

$\begin{equation} T \overset{d}{=} \text{Gamma}(1, \theta) \end{equation}$

Proofs

Proof 0

Let

$T \in \text{Exponential}(\theta)$ be an D214: Exponential random positive real number.

This result is a particular case of R5243: Finite sum of uncorrelated identically distributed exponential random positive real numbers is a gamma random random positive real number.

$\square$