Student-t-Verteilung 
p-Quantil t(p,nue)

Hermann.Singer@FernUni-Hagen.de

Manipulate[
a=5;
f=PDF[dist=StudentTDistribution[nue],x];
xq=Quantile[dist,p];

Show[
Plot[{f},{x,-a,xq},Filling->0,PlotRange->All,AxesOrigin->{0,0},ColorFunction->Hue],
Plot[{f},{x,-a,a},Filling->None,PlotRange->All,AxesOrigin->{0,0},ColorFunction->(GrayLevel[0 #]&)],
PlotLabel->"t-Verteilung: nue = "<>ToString[nue]<>", p-Quantil: p = "<>ToString[p]<>",  xp = "<>ToString[xq],
PlotRange->{{-a,a},{0,.5}},ImageSize->600
]

,{{p,.95},{.01,.025,.05,.1,.5,.75,.9,.95,.975,.99,.995,.999},ControlType->RadioButton},
{nue,3,50,1}]