# Exponential distribution

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Parameters Probability density function Cumulative distribution function ${\displaystyle \lambda >0,}$ rate, or inverse scale ${\displaystyle x\in [0,\infty )}$ ${\displaystyle \lambda e^{-\lambda x}}$ ${\displaystyle 1-e^{-\lambda x}}$ ${\displaystyle -{\frac {\ln(1-p)}{\lambda }}}$ ${\displaystyle {\frac {1}{\lambda }}}$ ${\displaystyle {\frac {\ln 2}{\lambda }}}$ ${\displaystyle 0}$ ${\displaystyle {\frac {1}{\lambda ^{2}}}}$ Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "http://localhost:6011/en.wikipedia.org/v1/":): 2 ${\displaystyle 6}$ ${\displaystyle 1-\ln \lambda }$ ${\displaystyle {\frac {\lambda }{\lambda -t}},{\text{ for }}t<\lambda }$ ${\displaystyle {\frac {\lambda }{\lambda -it}}}$ ${\displaystyle {\frac {1}{\lambda ^{2}}}}$ ${\displaystyle \ln {\frac {\lambda _{0}}{\lambda }}+{\frac {\lambda }{\lambda _{0}}}-1}$