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Exponential Distribution

NIST/SEMATECH Section 1.3.6.6.7 Exponential Distribution

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Exp(1) PDF 0 1 2 3 4 5 x 0 0.2 0.4 0.6 0.8 1 f(x)

CDF

Exp(1) CDF 0 1 2 3 4 5 x 0 0.2 0.4 0.6 0.8 1 F(x)

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CDF

Formulas

Probability Density Function

f(x)=λ e−λx,x≥0f(x) = \lambda\, e^{-\lambda x}, \quad x \ge 0

Cumulative Distribution Function

F(x)=1−e−λx,x≥0F(x) = 1 - e^{-\lambda x}, \quad x \ge 0

Properties

Mean

1λ\frac{1}{\lambda}

Variance

1λ2\frac{1}{\lambda^2}

Overview

The exponential distribution models the time between events in a Poisson process with rate λ\lambda. It is a one-parameter distribution commonly used for reliability analysis and waiting time problems.

Related Distributions

Gamma Distribution Weibull Distribution Poisson Distribution