Given a random variable X with probability density function $f$, the Support function will find a set A of real numbers such that $f\left(x\right)=0$ for all $x$ not in A. This set can be used to estimate the size of the support of X.

There are three forms of output that Support can return.

If called with the $\mathrm{output}=\mathrm{property}$ option, then Support returns a property that points in the set A have, typically of the form RealRange(a, b). Note that only numeric ranges can be represented in this way.

If called with the $\mathrm{output}=\mathrm{boolean}$ option, then Support returns a boolean expression expressing that t is in A, typically of the form $a\le t<b$.

If called with the $\mathrm{output}=\mathrm{range}$ option, then Support returns a range describing A, of the form $a..b$.

If called without an $\mathrm{output}$ option, then the default is the $\mathrm{property}$ format if t is not given and $\mathrm{boolean}$ format if t is given.

The first parameter can be a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).

The second parameter can be any algebraic expression. It is a necessary argument for $\mathrm{output}=\mathrm{boolean}$ and ignored otherwise.

$\mathrm{with}\left(\mathrm{Statistics}\right)\&colon;$

$\mathrm{Support}\left(\mathrm{Normal}\left(3\&comma;1\right)\right)$

$\mathrm{real}$

$\mathrm{Support}\left(\mathrm{Normal}\left(3\&comma;1\right)\&comma;'\mathrm{output}=\mathrm{range}'\right)$

$-\mathrm{\infty }..\mathrm{\infty }$

$\mathrm{Support}\left(\mathrm{Uniform}\left(3\&comma;5\right)\right)$

$\left[3\&comma;5\right)$

$\mathrm{Support}\left(\mathrm{Binomial}\left(10\&comma;0.5\right)\right)$

$\left[0\&comma;10\right]$

$\mathrm{Support}\left(\mathrm{Uniform}\left(3\&comma;5\right)\&comma;t\right)$

$3\le t<5$

$\mathrm{Support}\left(\mathrm{Uniform}\left(3\&comma;5\right)\&comma;4\right)$

$\mathrm{true}$

$\mathrm{Support}\left(\mathrm{Uniform}\left(3\&comma;5\right)\&comma;7\right)$

$\mathrm{false}$

$T≔\mathrm{Distribution}\left(\mathrm{`=`}\left(\mathrm{PDF}\&comma;t\mapsto \mathrm{piecewise}\left(t<\mathrm{-1}\&comma;0\&comma;t<1\&comma;\frac{3\cdot t^2\cdot \left(5-t\right)}{10}\&comma;0\right)\right)\right)\&colon;$

$X≔\mathrm{RandomVariable}\left(T\right)\&colon;$

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

$\left[\mathrm{-1}\&comma;1\right)$

$\mathrm{Support}\left(X\&comma;t\right)$

$\mathrm{-1}\le t<1$

$\mathrm{Support}\left(X\&comma;t\&comma;'\mathrm{output}=\mathrm{property}'\right)$

$\left[\mathrm{-1}\&comma;1\right)$

$\mathrm{Support}\left(X\&comma;t\&comma;'\mathrm{output}=\mathrm{boolean}'\right)$

$\mathrm{-1}\le t<1$

$\mathrm{Support}\left(X\&comma;t\&comma;'\mathrm{output}=\mathrm{range}'\right)$

$\mathrm{-1}..1$

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

The output option was introduced in Maple 16.

For more information on Maple 16 changes, see Updates in Maple 16.