Index: The Book of Statistical ProofsProbability 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.

Sources:

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