Index: The Book of Statistical Proofs ▷ Probability Distributions ▷ Univariate continuous distributions ▷ Exponential distribution ▷ Probability density function

Theorem: Let $X$ be a non-negative random variable following an exponential distribution:

\[\label{eq:exp} X \sim \mathrm{Exp}(\lambda) \; .\]

Then, the probability density function of $X$ is

\[\label{eq:gam-pdf} f_X(x) = \lambda \exp[-\lambda x] \; .\]

Proof: This follows directly from the definition of the exponential distribution.

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Metadata: ID: P46 | shortcut: exp-pdf | author: JoramSoch | date: 2020-02-08, 23:53.