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{MPLTEXT 1 0 21 "with(LinearAlgebra):\n" }{MPLTEXT 1 0 18 "with(Statis
tics):\n" }{MPLTEXT 1 0 23 "for dim from 1 to 2 do\n" }{MPLTEXT 1 0
28 " sigma:=[seq(1,i=1..dim)];\n" }{MPLTEXT 1 0 22 " C:=Matrix(dim,d
im):\n" }{MPLTEXT 1 0 25 " for i from 1 to dim do\n" }{MPLTEXT 1 0
15 " C[i,i]:=1;\n" }{MPLTEXT 1 0 6 " od:\n" }{MPLTEXT 1 0 25 " fo
r i from 2 to dim do\n" }{MPLTEXT 1 0 20 " C[i-1, i]:=1/4;\n" }
{MPLTEXT 1 0 20 " C[i, i-1]:=1/4;\n" }{MPLTEXT 1 0 6 " od:\n" }
{MPLTEXT 1 0 25 " for i from 1 to dim do\n" }{MPLTEXT 1 0 27 " for
j from 1 to dim do\n" }{MPLTEXT 1 0 48 " C[i, j] := C[i, j] * si
gma[i] * sigma[j];\n" }{MPLTEXT 1 0 8 " od:\n" }{MPLTEXT 1 0 6 " o
d:\n" }{MPLTEXT 1 0 27 " x:=<seq(X[i],i=1..dim)>:\n" }{MPLTEXT 1 0
84 " f:=1/(2*Pi)^(dim/2)/sqrt(Determinant(C))*exp(-Transpose(x).Matri
xInverse(C).x/2):\n" }{MPLTEXT 1 0 71 " print(evalf(subs(seq(X[i]=Qua
ntile(Normal(0,1),u[i]),i=1..dim),f)));\n" }{MPLTEXT 1 0 98 " print(e
valf(subs(seq(X[i]=Quantile(Normal(0,1),u[i]),i=1..dim),[seq(diff(f,X[
j]),j=1..dim)])));\n" }{MPLTEXT 1 0 33 " cdf:=(combine(expand(f),exp)
):\n" }{MPLTEXT 1 0 16 " A:=-infinity:\n" }{MPLTEXT 1 0 25 " for i f
rom 1 to dim do\n" }{MPLTEXT 1 0 54 " cdf:=Int(cdf,X[i]=A..Quantile
(Normal(0,1),u[i]));\n" }{MPLTEXT 1 0 6 " od:\n" }{MPLTEXT 1 0 14 " \+
print(cdf);\n" }{MPLTEXT 1 0 3 "od;" }}{PARA 11 "" 1 "" {XPPMATH 20 "7
#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I'MatrixG6$%*protectedGI(_sy
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}}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(\"\"##\"\"\"F$I#PiG%*protectedG#!
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{PARA 11 "" 1 "" {XPPMATH 20 ",$I)infinityG%*protectedG!\"\"" }}{PARA
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}}{PARA 11 "" 1 "" {XPPMATH 20 "7$\"\"\"F#" }}{PARA 11 "" 1 ""
{XPPMATH 20 "-I'MatrixG6$%*protectedGI(_syslibG6\"6#/I$%idGF'\"0)))='p
D:S\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-&I'VectorG6$%*protectedGI(_sys
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{XPPMATH 20 ",$*(I#PiG%*protectedG!\"\"\"#:#\"\"\"\"\"#-I$expG6$F%I(_s
yslibG6\"6#,&*&&I\"XGF/6#F)F),&F3#\"#;F'&F46#F*#!\"%F'F)#F&F**&F9F),&F
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ctedGI(_syslibG6\"6#,&*&-I'RootOfGF%6#,(-I$erfGF%6#I#_ZGF%!\"\"F4\"\"
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{XPPMATH 20 "7$,$*&,&-I'RootOfG6$%*protectedGI(_syslibG6\"6#,(-I$erfGF
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}{PARA 11 "" 1 "" {XPPMATH 20 ",$*(I#PiG%*protectedG!\"\"\"#:#\"\"\"\"
\"#-I$expG6$F%I(_syslibG6\"6#,(*$&I\"XGF/6#F)F*#!\")F'*&F3F)&F46#F*F)#
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*protectedG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "-I$IntG6$%*protected
GI(_syslibG6\"6$-F#6$,$*(I#PiGF%!\"\"\"#:#\"\"\"\"\"#-I$expGF$6#,(*$&I
\"XGF'6#F1F2#!\")F/*&F8F1&F96#F2F1#\"\"%F/*$F>F2F;F1#F2F//F8;,$I)infin
ityGF%F.*&-I'RootOfGF$6#,(-I$erfGF$6#I#_ZGF$F.F.F1&I\"uGF'F:F2F1F2F0/F
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{MPLTEXT 1 0 32 "pdf:=diff(diff(cdf,u[1]),u[2]);\n" }{MPLTEXT 1 0 36 "
evalf(subs(u[1]=0.2,u[2]=0.2,pdf));\n" }{MPLTEXT 1 0 36 "evalf(subs(u[
1]=0.2,u[2]=0.2,cdf));\n" }}{PARA 11 "" 1 "" {XPPMATH 20 ",$**-I$expG6
$%*protectedGI(_syslibG6\"6#,$*$-I'RootOfGF&6#,(-I$erfGF&6#I#_ZGF&!\"
\"F5\"\"\"&I\"uGF)6#\"\"#F:F:F5F5-F%6#,$*$-F.6#,(F1F5F5F6&F86#F6F:F:F5
F5\"#:#F6F:-F%6#,(F>#!#;FD*&F?F6F-F6#\"\")FDF,FIF6#\"\"%FD" }}{PARA 11
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"$\"+=TiRh!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "PDF_:=pro
c(x,y)\n" }{MPLTEXT 1 0 33 " evalf(subs(u[1]=x,u[2]=y,pdf))\n" }
{MPLTEXT 1 0 4 "end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "eps
:=1e-1:\n" }{MPLTEXT 1 0 21 "for i from 2 to 9 do\n" }{MPLTEXT 1 0 16
" eps:=0.1*eps:\n" }{MPLTEXT 1 0 96 " print([eps,i,evalf[i](Int(Int(
(u[1]-1/2)*(u[2]-1/2)*pdf,u[1]=eps..1-eps),u[2]=eps..1-eps))]);\n" }
{MPLTEXT 1 0 4 "od:\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%$\"\"\"!\"#\"
\"#$\"#<!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%$\"\"\"!\"$\"\"$$\"$&>
!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%$\"\"\"!\"%\"\"%^$$\"%*)>!\"&$
\"%CB!#D" }}{PARA 11 "" 1 "" {XPPMATH 20 "7%$\"\"\"!\"&\"\"&-I$IntG6$%
*protectedGI(_syslibG6\"6$-F(6$,$*,,&&I\"uGF,6#F$F$$!&++&F%F$F$,&&F46#
\"\"#F$F6F$F$-I$expGF)6#,$*$-I'RootOfGF)6#,(-I$erfGF)6#I#_ZGF)!\"\"FIF
$F9F;F;$FI\"\"!FI-F=6#,$*$-FB6#,(FEFIFIF$F3F;F;FJFI-F=6#,(FO$!&n1\"!\"
%*&FPF$FAF$$\"&LL&F%F@FVF$$\"&G.\"FX/F3;F#$\"&*****F%/F9Fin" }}{PARA
207 "" 1 "" {TEXT 208 0 "" }{HYPERLNK 208 "Warning, computation inter
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "inf:=1.0:\n" }{MPLTEXT 1 0
23 "for i from 1 to 100 do\n" }{MPLTEXT 1 0 16 " inf:=inf+1.0:\n" }
{MPLTEXT 1 0 13 "Digits:=2*i;\n" }{MPLTEXT 1 0 134 " print([inf,evalf
[2*i](Int(Int((CDF(Normal(0,1),s)-1/2)*(CDF(Normal(0,1),t)-1/2)*subs(X
[1]=s,X[2]=t,f),s=-inf..inf),t=-inf..inf))]);\n" }{MPLTEXT 1 0 3 "od:"
}}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"#?!\"\"$\"#8!\"$" }}{PARA 11 ""
1 "" {XPPMATH 20 "7$$\"#I!\"\"$\"%O>!\"&" }}{PARA 11 "" 1 "" {XPPMATH
20 "7$$\"#S!\"\"$\"'\"H*>!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"#]
!\"\"$\")ej%*>!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"#g!\"\"$\"+7V
l%*>!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"#q!\"\"$\"-k$QaY*>!#8" }
}{PARA 11 "" 1 "" {XPPMATH 20 "7$$\"#!)!\"\"$\"/%QPQaY*>!#:" }}{PARA
207 "" 1 "" {TEXT 208 0 "" }{HYPERLNK 208 "Warning, computation inter
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}
{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2
33 1 1 }
|
