> restart:
> Digits:=20:
> with(Statistics):
> X1:=RandomVariable(Uniform(-1,2)):
> CDF1:=CDF(X1,x1):
> X2:=RandomVariable(Gamma(1/2,2)):
> CDF2:=CDF(X2,x2):
> X3:=RandomVariable(Beta(r,t-r)):
> CDF3:=subs(t3=((x3+1)/3),r=2,t=5,CDF(X3,t3)):
> QDF1:=proc(q)
>   fsolve(CDF1=q,x1)
> end:
> QDF2:=proc(q)
>   fsolve(CDF2=q,x2)
> end:
> QDF3:=proc(q)
>   fsolve(CDF3=q,x3)
> end:
> vars:=Su1,S2,S3:
> fcns:=S1,S2,S3:
> S:=array(1..3):
> X:=[QDF1,CDF2,CDF3]:
> DT:=array(1..3,1..3):
> D2T:=array(1..3,1..3,1..3):
> T1:=evalf(subs(u=CDF1,PHIInv)):
> T2:=evalf(subs(u=CDF2,PHIInv)):
> T3:=evalf(subs(u=CDF3,PHIInv)):
> for i from 1 to 3 do
>   T[i] := fcns[i]:
> od:
> for i from 1 to 3 do
>   for j from 1 to 3 do
>     DT[i, j] := diff(fcns[j], vars[i]):
>   od:
> od:
> for i from 1 to 3 do
>   for j from 1 to 3 do
>     for k from 1 to 3 do
>       D2T[i, j, k] := diff(diff(fcns[k],vars[j]), vars[i]):
>     od:
>   od:
> od:
> print(map(_x->evalf(subs(x1=1.0,x2=1.0,x3=1.0,_x)),U));
> print(map(_x->evalf(subs(x1=1.0,x2=1.0,x3=1.0,_x)),T));
> print(map(_x->evalf(subs(x1=1.0,x2=1.0,x3=1.0,_x)),DT));
> print(map(_x->evalf(subs(x1=1.0,x2=1.0,x3=1.0,_x)),D2T));
> evalf(subs(x3=1,diff(CDF3,x3$2)));

  [0.66666666666666666666, 0.59399415029016192433,

        0.88888888888888888888]


  [0.43072729929545749018, 0.23783161172327289982,

        1.2206403488473496984]


                  [0.91675891062085696982 , 0. , 0.]
                  [                                ]
                  [0. ,  1.3958657499972168874 , 0.]
                  [                                ]
                  [0. ,  0. , 1.5644348483337176127]


  array(1 .. 3, 1 .. 3, 1 .. 3, [

        (1, 1, 1) = 0.36200342352556526451

        (1, 1, 2) = 0.

        (1, 1, 3) = 0.

        (1, 2, 1) = 0.

        (1, 2, 2) = 0.

        (1, 2, 3) = 0.

        (1, 3, 1) = 0.

        (1, 3, 2) = 0.

        (1, 3, 3) = 0.

        (2, 1, 1) = 0.

        (2, 1, 2) = 0.

        (2, 1, 3) = 0.

        (2, 2, 1) = 0.

        (2, 2, 2) = -0.93246484095220475381

        (2, 2, 3) = 0.

        (2, 3, 1) = 0.

        (2, 3, 2) = 0.

        (2, 3, 3) = 0.

        (3, 1, 1) = 0.

        (3, 1, 2) = 0.

        (3, 1, 3) = 0.

        (3, 2, 1) = 0.

        (3, 2, 2) = 0.

        (3, 2, 3) = 0.

        (3, 3, 1) = 0.

        (3, 3, 2) = 0.

        (3, 3, 3) = 0.6408117548914454467

        ])


                       -0.44444444444444444447

> 
