The uniform distribution is a continuous probability random variable with probability density function given by:

subject to the following conditions:

The uniform variate is related to the unit parameter Beta variate by Uniform(0,1) ~ Beta(1,1).

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

$X≔\mathrm{UniformRandomVariable}\left(a\,b\right)\:$

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

$\left\{\begin{array}{cc}0& u<a\\ \frac{1}{b-a}& u<b\\ 0& \mathrm{otherwise}\end{array}\right.$

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

$\left\{\begin{array}{cc}0.& 0.5<a\\ \frac{1}{b-1.a}& 0.5<b\\ 0.& \mathrm{otherwise}\end{array}\right.$

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

$\frac{a}{2}+\frac{b}{2}$

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

$\frac{{\left(b-a\right)}^2}{12}$

$Y≔\mathrm{UniformRandomVariable}\left(-1\&comma;1\right)\&colon;$

$\mathrm{PDF}\left(Y\&comma;x\&comma;\mathrm{output}=\mathrm{plot}\right)$

$\mathrm{CDF}\left(Y\&comma;x\right)$

$\left\{\begin{array}{cc}0& x<\mathrm{-1}\\ \frac{x}{2}+\frac{1}{2}& x<1\\ 1& \mathrm{otherwise}\end{array}\right.$

$\mathrm{CDF}\left(Y\&comma;0.5\&comma;\mathrm{output}=\mathrm{plot}\right)$

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

Johnson, Norman 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.

The Student[Statistics][UniformRandomVariable] command was introduced in Maple 18.

For more information on Maple 18 changes, see Updates in Maple 18.