The Specialize function takes a random variable or distribution data structure that contains symbolic parameters, and performs a substitution to specialize the given random variable or distribution.

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

$X≔\mathrm{RandomVariable}\left(\mathrm{Normal}\left(a\,b\right)\right)$

$X≔\mathrm{\_R}$

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

$a,b$

$\mathrm{X1}≔\mathrm{Specialize}\left(X\,a=0\right)$

$\mathrm{X1}≔\mathrm{\_R0}$

$\mathrm{Mean}\left(\mathrm{X1}\right),\mathrm{StandardDeviation}\left(\mathrm{X1}\right)$

$0,b$

$\mathrm{X2}≔\mathrm{Specialize}\left(X\,\left[a=c\,b=c^2\right]\right)$

$\mathrm{X2}≔\mathrm{\_R1}$

$\mathrm{Mean}\left(\mathrm{X2}\right),\mathrm{StandardDeviation}\left(\mathrm{X2}\right)$

$c,c^2$

$Y≔X+b\mathrm{X2}$

$Y≔\mathrm{\_R1}b+\mathrm{\_R}$

$\mathrm{Mean}\left(Y\right),\mathrm{StandardDeviation}\left(Y\right)$

$bc+a,\sqrt{b^2{c}^4+b^2}$

$\mathrm{Y1}≔\mathrm{Specialize}\left(Y\,b=a\right)$

$\mathrm{Y1}≔\mathrm{\_R1}a+\mathrm{\_R2}$

$\mathrm{Mean}\left(\mathrm{Y1}\right),\mathrm{StandardDeviation}\left(\mathrm{Y1}\right)$

$ac+a,\sqrt{a^2{c}^4+a^2}$

$\mathrm{Specialize}\left(X\,b=-1\right)$

Error, (in Statistics:-Specialize) invalid parameters obtained when substituting [b = -1]

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