Exponential Distribution

The exponential probability density function for a random variable $X$ is given by

f_{X} (x) = λ \exp (- λ x) λ > 0,

where the parameter $λ$ is a scale parameter. The exponential distribution function is

F_{X} (x) = 1 - \exp (- λ x) λ > 0.

The mean value and standard deviation of the random variable $X$ for the exponential distribution are given by

μ_{X} = σ_{X} = \frac{1}{λ} .

The exponential probability density function, as shown in the figure below, is often used to describe usage life of components.