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The Maxwell distribution is a continuous probability distribution with probability density function given by:

subject to the following conditions:

Note that the Maxwell command is inert and should be used in combination with the RandomVariable command.

$\mathrm{with}\left(\mathrm{Statistics}\right)\:$

$X≔\mathrm{RandomVariable}\left(\mathrm{Maxwell}\left(\mathrm{\alpha }\right)\right)\:$

$\mathrm{PDF}\left(X\,u\right)$

$\left\{\begin{array}{cc}0& u<0\\ \frac{\sqrt{2}\sqrt{\frac{1}{\mathrm{\pi }}}{u}^2{\&ExponentialE;}^{-\frac{u^2}{2{\mathrm{\alpha }}^2}}}{{\mathrm{\alpha }}^3}& \mathrm{otherwise}\end{array}\right.$

$\mathrm{PDF}\left(X\&comma;0.5\right)$

$\frac{0.1994711401{\&ExponentialE;}^{-\frac{0.1250000000}{{\mathrm{\alpha }}^2}}}{{\mathrm{\alpha }}^3}$

$\mathrm{Mean}\left(X\right)$

$\frac{2\sqrt{2}\mathrm{\alpha }}{\sqrt{\mathrm{\pi }}}$

$\mathrm{Variance}\left(X\right)$

$\frac{{\mathrm{\alpha }}^2\left(3\mathrm{\pi }-8\right)}{\mathrm{\pi }}$

Evans, Merran; Hastings, Nicholas; and Peacock, Brian. Statistical Distributions. 3rd ed. Hoboken: Wiley, 2000.

Johnson, Normal L.; Kotz, Samuel; and Balakrishnan, N. Continuous Univariate Distributions. 2nd ed. 2 vols. Hoboken: Wiley, 1995.

Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.