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{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "f:=exp(-(x-mu)^2/2/s
igma^2)/sqrt(2*Pi)/sigma;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG,$*
&#\"\"\"\"\"#F(**-%$expG6#,$*(F)!\"\",&%\"xGF(%#muGF0F)%&sigmaG!\"#F0F
(F)F'%#PiG#F0F)F4F0F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "
assume(sigma>0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "int(f,x
=-infinity..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "int(f*exp(t*x),x=-infinity..
infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$expG6#,$*(\"\"#!\"\"%
\"tG\"\"\",&*&F(F+%#muGF+F+*&F*F+)%'sigma|irGF(F+F+F+F+" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "f:=exp(-(z1^2+z2^2-2*rho*z1*z2)/2/(
1-rho^2))/2/Pi/sqrt(1-rho^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"f
G,$*&#\"\"\"\"\"#F(*(-%$expG6#,$*(F)!\"\",(*$)%#z1GF)F(F(*$)%#z2GF)F(F
(**F)F(%$rhoGF(F4F(F7F(F0F(,&F(F(*$)F9F)F(F0F0F0F(%#PiGF0F:#F0F)F(F(" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "assume(rho^2<1);" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "int(int(f,z1=-infinity..infi
nity),z2=-infinity..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"
\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "int(int(f*exp(z1*t1+z
2*t2),z1=-infinity..infinity),z2=-infinity..infinity);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#-%$expG6#,(*&#\"\"\"\"\"#F)*$)%#t1GF*F)F)F)*(%%rho
|irGF)F-F)%#t2GF)F)*&F(F)*$)F0F*F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 59 "C:=matrix(3,3,[1,rho12,rho13,rho12,1,rho23,rho13,rho2
3,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"CG-%'matrixG6#7%7%\"\"\"
%&rho12G%&rho13G7%F+F*%&rho23G7%F,F.F*" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning
, the protected names norm and trace have been redefined and unprotect
ed\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "Cinv:=inverse(C):" 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "jv:=evalm([z1,z2,z3]&*Cin
v&*[z1,z2,z3])-z1^2;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%#jvG,**&,(*(
%#z1G\"\"\",&F*!\"\"*$)%&rho23G\"\"#F*F*F*,,F*F,F-F**$)%&rho12GF0F*F**
*F0F*F4F*%&rho13GF*F/F*F,*$)F6F0F*F*F,F**(%#z2GF*,&F4F,*&F6F*F/F*F*F*F
1F,F,*(%#z3GF*,&*&F4F*F/F*F*F6F,F*F1F,F,F*F)F*F**&,(*(F)F*F;F*F1F,F,*(
F:F*,&F*F,F7F*F*F1F,F**(F>F*,&F/F**&F4F*F6F*F,F*F1F,F*F*F:F*F**&,(*(F)
F*F?F*F1F,F,*(F:F*FGF*F1F,F**(F>F*,&F*F,F2F*F*F1F,F*F*F>F*F**$)F)F0F*F
," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "aux2:=(z2-z1*rho12)/sq
rt(1-rho12^2); aux3:=(z3-z1*rho13)/sqrt(1-rho13^2);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%%aux2G*&,&%#z2G\"\"\"*&%#z1GF(%&rho12GF(!\"\"F(,&F(
F(*$)F+\"\"#F(F,#F,F0" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%aux3G*&,&%
#z3G\"\"\"*&%#z1GF(%&rho13GF(!\"\"F(,&F(F(*$)F+\"\"#F(F,#F,F0" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "Rho:=(rho23-rho12*rho13)/sqr
t(1-rho12^2)/sqrt(1-rho13^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$Rh
oG*(,&%&rho23G\"\"\"*&%&rho12GF(%&rho13GF(!\"\"F(,&F(F(*$)F*\"\"#F(F,#
F,F0,&F(F(*$)F+F0F(F,F1" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "
jv-(aux2^2+aux3^2-2*aux2*aux3*Rho)/(1-Rho^2):" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "det(C)-(1-Rho^2)*(
1-rho12^2)*(1-rho13^2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "
simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "jv:=randmatrix(5,5):" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "V:=evalm(jv&*transpose(jv)):  C:=ma
trix(5,5):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "for i to 5 do
 for j to 5 do C[i,j]:=evalf(V[i,j]/sqrt(V[i,i]*V[j,j])) end do end do
:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalm(C);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%'matrixG6#7'7'$\"\"\"\"\"!$\"+^p*RS$!#5$\"+z2o
nKF-$\"+]`3uRF-$\"+vn<)p#F-7'F+F($\"+%RgZ+#F-$!+3OE^OF-$!+a!3GX\"F-7'F
.F5F($!+1#H*>[F-$!+x>(\\W(F-7'F0F7F<F($\"+rK4OsF-7'F2F9F>FAF(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "part1:=proc(C,i,j,k): (C[i,j
]-C[i,k]*C[j,k])/sqrt(1-C[i,k]^2)/sqrt(1-C[j,k]^2) end:" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "part1(C,1,2,3);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#$\"+9V%)oH!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 125 "part2:=proc(C,i,j,k,m): (part1(C,i,j,k)-part1(C,i,m,k)*part1(
C,j,m,k))/sqrt(1-part1(C,i,m,k)^2)/sqrt(1-part1(C,j,m,k)^2) end:" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "part2(C,1,2,3,4);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#$\"+]T>%=(!#5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 17 "part2(C,2,1,4,3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
$\"+\\T>%=(!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "part2(C,1
,3,2,4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++Z$4j(!#5" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "18 0 0" 0 }{VIEWOPTS 1 
1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }