> restart:
> with(Statistics):
> X:=Uniform(0,1):
> pdf:=PDF(X,x)*PDF(X,y)*PDF(X,z):
> pdf_x:=int(int(pdf,y=0..1),z=0..1):
> pdf_y:=int(int(pdf,z=0..1),x=0..1):
> pdf_z:=int(int(pdf,x=0..1),y=0..1):
> pdf:=pdf_x*pdf_y*pdf_z:
> ddf:=[diff(pdf,x),diff(pdf,y),diff(pdf,z)]:
> mean:=[int(x*pdf_x,x=0..1),int(y*pdf_y,y=0..1),int(z*pdf_z,z=0..1)]:
> covariance:=array(1..3,1..3):
> fct:=[pdf_x,pdf_y,pdf_z]:
> var:=[x,y,z]:
> for i from 1 to 3 do
>   for j from 1 to 3 do
>    
> covariance[i,j]:=int(int((var[i]-mean[i])*(var[j]-mean[j])*fct[i]*fct[
> j],var[i]=0..1),var[j]=0..1);
>   od:
> od:
> cdf:=subs(u=x,v=y,w=z,int(int(int(pdf,x=0..u),y=0..v),z=0..w)):
> assume(t>0,t<1):
> qdf:=subs(x=t,y=t,z=t,cdf):
> valnum:=x=0.6,y=0.6,z=0.6:
> evalf(subs(valnum,ddf));
> evalf(subs(valnum,pdf));
> evalf(subs(valnum,cdf));
> evalf(fsolve(subs(valnum,qdf)=0.95,t));
> evalf(subs(valnum,mean));
> evalf(map(_x->subs(valnum,_x),covariance));

                             [0., 0., 0.]


                                  1.


                                0.216


                             0.9830475725


              [0.5000000000, 0.5000000000, 0.5000000000]


          [0.08333333333         0.               0.      ]
          [                                               ]
          [     0.          0.08333333333         0.      ]
          [                                               ]
          [     0.               0.          0.08333333333]

> 
