{VERSION 4 0 "IBM INTEL LINUX22" "4.0" }
{USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 0 0 255 1 0 2 0 
0 1 0 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 
0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 
1 }{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 }{PSTYLE "Normal
" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 
1 0 0 0 0 3 0 3 0 2 2 0 1 }{PSTYLE "Text Output" -1 2 1 {CSTYLE "" -1 
-1 "Courier" 1 10 0 0 255 1 0 0 0 0 0 1 3 0 3 0 }1 0 0 -1 -1 -1 0 0 0 
0 0 0 -1 0 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 
0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 3 0 3 0 2 2 0 1 }{PSTYLE "" 
2 6 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 2 0 0 0 }0 0 0 -1 
-1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Warning" 2 7 1 {CSTYLE "" -1 -1 "" 0 
1 0 0 255 1 0 0 0 0 0 0 1 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }
{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 
0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 12 1 
{CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 
0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 
0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "R
3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Courier" 1 12 0 0 0 1 2 2 2 2 2 
2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "R3 Font 2" -1 257 1 
{CSTYLE "" -1 -1 "Times" 1 12 128 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 
0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 258 1 {CSTYLE "" -1 -1 "Times
" 1 16 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }
{PSTYLE "Title" -1 259 1 {CSTYLE "" -1 -1 "Times" 1 36 0 0 0 1 2 1 2 
2 2 2 1 1 1 1 }3 1 0 0 12 12 3 0 3 0 2 2 19 1 }{PSTYLE "Title" -1 260 
1 {CSTYLE "" -1 -1 "Times" 1 48 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 
12 12 3 0 3 0 2 2 19 1 }}
{SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG 
{PARA 260 "" 0 "" {TEXT -1 23 "Aide \340 la d\351cision (17)" }}}
{SECT 1 {PARA 3 "" 0 "" {TEXT -1 12 "D\351clarations" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 24 "kernelopts(ASSERT=true);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#%&falseG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 68 "with(stats); with(transform); with(statplots); with(plots, displ
ay):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7*%&anovaG%)describeG%$fitG%+i
mportdataG%'randomG%*statevalfG%*statplotsG%*transformG" }}{PARA 7 "" 
1 "" {TEXT -1 69 "Warning, the protected name apply has been redefined
 and unprotected\n" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#72%&applyG%*clas
smarkG%4cumulativefrequencyG%.deletemissingG%)dividebyG%*frequencyG%'m
ovingG%+multiapplyG%,scaleweightG%&splitG%.standardscoreG%)statsortG%*
statvalueG%-subtractfromG%&tallyG%*tallyintoG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7.%(boxplotG%*histogramG%,scatterplotG%'xscaleG%'xshift
G%+xyexchangeG%+xzexchangeG%'yscaleG%'yshiftG%+yzexchangeG%'zscaleG%'z
shiftG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "with(pldx); with(
simul);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\\ppldx~v6-20~~;~~author~:
~<douillet@ensait.fr>~~;~~last~modif~(V6)~:~Tue~27/05/2003G" }}{PARA 
12 "" 1 "" {XPPMATH 20 "6#7@%&XtensG%+convert/D2G%,ever_loadedG%'isdia
gG%'sinsinG%*xHospitalG%'xcloneG%%xcolG%&xcol3G%)xcollectG%'xcolorG%$x
csG%(xdchvarG%%xeigG%&xeiggG%)xfenetreG%(xfubiniG%&xjoliG%.xmanip_somm
esG%(xmk_pivG%&xplifG%'xpurgeG%%xputG%+xreg_falsiG%)xres_iniG%)xrevers
eG%&xtensG%&xtreeG%&xtrigG%0zmanip_productsG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#%]psimul~v6-10~~;~~author~:~<douillet@ensait.fr>~~;~~la
st~modif~(V6)~:~Fri~24/01/2003G" }}{PARA 7 "" 1 "" {TEXT -1 49 "Warnin
g, the name ever_loaded has been redefined\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7'%)chi2_tstG%,ever_loadedG%&histoG%*histo_arrG%'xtally
G" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 29 "Lancer d'une pi\350ce \351
quilibr\351e" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "nn:=40; ra:=
 rand(2): " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#nnG\"#S" }}}{EXCHG 
{PARA 0 "" 0 "" {MPLTEXT 0 21 17 "li:= ['ra()'$nn];" }{TEXT -1 0 "" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "li1 := [0, 0, 1, 0, 1, 1, 0, 0, 1,
 1, 0, 1, 1, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 0, 1, \+
1, 0, 0, 0, 0, 0, 1, 0]; li:= li1:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%$li1G7J\"\"!F&\"\"\"F&F'F'F&F&F'F'F&F'F'F&F&F&F&F&F'F&F&F'F'F'F'F&F'
F&F'F'F&F'F'F&F&F&F&F&F'F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "pil
e ou face" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "mu:=1/2;\nsigma2:= add
((k-1/2)^2*(1/2),k=0..1);\nM4:= add((k-1/2)^4*(1/2),k=0..1);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#muG#\"\"\"\"\"#" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%'sigma2G#\"\"\"\"\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 
"6#>%#M4G#\"\"\"\"#;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "test de m
_e" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "m_e:= add(k, k=li)/nn; \nesp,
var:= mu, sigma2/nn; \nz_m:= evalf((m_e-(esp))/sqrt(var));" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$m_eG#\"\"*\"#?" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>6$%$espG%$varG6$#\"\"\"\"\"##F)\"$g\"" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%$z_mG$!+?`bCj!#5" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 12 "test de v_e " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "v_e:=
 m_e-m_e^2;\nesp,var:= sigma2, (M4-(nn-3)/(nn-1)*sigma2^2)/nn;\nz_v:= \+
evalf((v_e-(esp))/sqrt(var)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$v
_eG#\"#**\"$+%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6$%$espG%$varG6$#\"
\"\"\"\"%#F)\"&![7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$z_vG$!+3![Gz#
!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 32 "\351valuation de l'auto-co
rr\351lation" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "s1, sx, sxx, sy, s
yy, sxy :=nn-1. ,\nadd(li[k],k=1..nn-1), add(li[k]^2,k=1..nn-1),\nadd(
li[k],k=2..nn), add(li[k]^2,k=2..nn),\nadd(li[k]*li[k+1],k=1..nn-1);" 
}}{PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "mx:=sx/s1; my:=sy/s1; vx:=sxx/s1
-mx^2; vy:=syy/s1-my^2;\ncov:= sxy/s1-mx*my; rr:= cov/sqrt(vx*vy); frv
:= 1/(1-rr^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6(%#s1G%#sxG%$sxxG%
#syG%$syyG%$sxyG6($\"#R\"\"!\"#=F/F/F/\"\")" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#mxG$\"+:YQ:Y!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
%#myG$\"+:YQ:Y!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vxG$\"+,r?&[#!
#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vyG$\"+,r?&[#!#5" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#>%$covG$!)ja*)y!#5" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%#rrG$!+aJguJ!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%
$frvG$\"+F)35+\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "au
tres:= plot(nn/2,x=-0.5..1.5), tickmarks=[[0.0001=0,1=1], [nn/2]], lab
els=[``,``]:\ntallyinto(li, [-0.5..0.5, 0.5..1.5]); \ndisplay(histogra
m(%), autres);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$-%'WeightG6$;$!\"&
!\"\"$\"\"&F*\"#A-F%6$;F+$\"#:F*\"#=" }}{PARA 13 "" 1 "" {GLPLOT2D 
400 300 300 {PLOTDATA 2 "6'-%)POLYGONSG6%7&7$$!\"&!\"\"\"\"!7$F($\"+++
++A!\")7$$\"\"&F*F-7$F1F+7&F37$F1$\"+++++=F/7$$\"#:F*F67$F9F+-%&COLORG
6&%$RGBG$\"\"(F*F@$\"#5F*-%'CURVESG6$7S7$$!3++++++++]!#=$\"#?F+7$$!3pm
mm;p0kXFKFL7$$!3JLL$3<XZ=%FKFL7$$!3nmmmT%p\"ePFKFL7$$!3rmmm\"4m(GLFKFL
7$$!3\"QLL3i.9!HFKFL7$$!3\"ommT!R=0DFKFL7$$!3K++]P8#\\4#FKFL7$$!3*pmmT
?F1n\"FKFL7$$!3\\++](y$pZ7FKFL7$$!3vILLLyaE\")!#>FL7$$!39mmm;>s%H%FfoF
L7$$\"3::'******\\1!>!#@FL7$$\"3p)******\\Z/N%FfoFL7$$\"3\\*******\\$f
C&)FfoFL7$$\"3ELL$ez6:B\"FKFL7$$\"3Rmmm;=C#o\"FKFL7$$\"3-mmmm#pS1#FKFL
7$$\"3]****\\i`A3DFKFL7$$\"3slmmm(y8!HFKFL7$$\"3V++]i.tKLFKFL7$$\"39++
](3zMu$FKFL7$$\"3\"pmm;H_?<%FKFL7$$\"3dmm;zihlXFKFL7$$\"3;LLL3#G,*\\FK
FL7$$\"3pJL$ezw5V&FKFL7$$\"3(*)***\\PQ#\\\"eFKFL7$$\"3GKLLe\"*[HiFKFL7
$$\"3I*******pvxl'FKFL7$$\"3$z****\\_qn2(FKFL7$$\"3V)***\\i&p@[(FKFL7$
$\"3B)****\\2'HKzFKFL7$$\"3ElmmmZvO$)FKFL7$$\"3h******\\2go()FKFL7$$\"
3UKL$eR<*f\"*FKFL7$$\"3m******\\)Hxe*FKFL7$$\"3ckm;H!o-***FKFL7$$\"3))
***\\7k.6/\"!#<FL7$$\"3emmmT9C#3\"FitFL7$$\"3\"****\\i!*3`7\"FitFL7$$
\"3QLLL$*zym6FitFL7$$\"3GLL$3N1#47FitFL7$$\"3kmm\"HYt7D\"FitFL7$$\"3&*
******p(G**G\"FitFL7$$\"3lmm;9@BM8FitFL7$$\"3ELLL`v&QP\"FitFL7$$\"30++
DOl5;9FitFL7$$\"3/++v.Uac9FitFL7$$\"3++++++++:FitFL-%'COLOURG6&F?FB$F+
F+F^w-%+AXESLABELSG6$%!GFbw-%*AXESTICKSG6$7$/$\"\"\"!\"%F+/FiwFiw7#FM-
%%VIEWG6$;$!+++++q!#5$\"+++++<!\"*%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 15 
"Pi\350ce begayante" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 115 "rb:=
 proc() global mrb; \nif not assigned(mrb) then mrb:= ra() fi;\nif ra(
)=1 then mrb:= ra(); fi; \nreturn mrb;\nend: " }}}{EXCHG {PARA 0 "" 0 
"" {MPLTEXT 0 21 19 "li:= ['rb()'$nn];  " }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 138 "li2 := [0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1,
 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, \+
0, 0]; li:= li2:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$li2G7J\"\"!F&F&
F&F&F&F&\"\"\"F'F'F&F'F'F'F'F&F'F'F'F'F'F'F'F'F'F'F&F&F&F&F&F&F&F'F&F&
F&F&F&F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "test de m_e" }}{PARA 
0 "> " 0 "" {MPLTEXT 1 0 85 "m_e:= add(k, k=li)/nn; \nesp,var:= mu, si
gma2/nn; \nz_m:= evalf((m_e-(esp))/sqrt(var));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$m_eG#\"\"*\"#?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6
$%$espG%$varG6$#\"\"\"\"\"##F)\"$g\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%$z_mG$!+?`bCj!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "test de v
_e " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "v_e:= m_e-m_e^2;\nesp,var:=
 sigma2, (M4-(nn-3)/(nn-1)*sigma2^2)/nn;\nz_v:= evalf((v_e-(esp))/sqrt
(var)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$v_eG#\"#**\"$+%" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>6$%$espG%$varG6$#\"\"\"\"\"%#F)\"&![7
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$z_vG$!+3![Gz#!#5" }}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 32 "\351valuation de l'auto-corr\351lation" }
}{PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "s1, sx, sxx, sy, syy, sxy :=nn-1.
 ,\nadd(li[k],k=1..nn-1), add(li[k]^2,k=1..nn-1),\nadd(li[k],k=2..nn),
 add(li[k]^2,k=2..nn),\nadd(li[k]*li[k+1],k=1..nn-1);" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 115 "mx:=sx/s1; my:=sy/s1; vx:=sxx/s1-mx^2; vy:=syy/
s1-my^2;\ncov:= sxy/s1-mx*my; rr:= cov/sqrt(vx*vy); frv:= 1/(1-rr^2);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6(%#s1G%#sxG%$sxxG%#syG%$syyG%$sx
yG6($\"#R\"\"!\"#=F/F/F/\"#9" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#mxG
$\"+:YQ:Y!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#myG$\"+:YQ:Y!#5" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vxG$\"+,r?&[#!#5" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>%#vyG$\"+,r?&[#!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%$covG$\"+wgcf9!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#rrG$\"+we,
te!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$frvG$\"+i%Ql_\"!\"*" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "tallyinto(li, [-0.5..0.5, 0.
5..1.5]); \ndisplay(histogram(%), autres);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7$-%'WeightG6$;$!\"&!\"\"$\"\"&F*\"#A-F%6$;F+$\"#:F*\"#
=" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%)POLYGONS
G6%7&7$$!\"&!\"\"\"\"!7$F($\"+++++A!\")7$$\"\"&F*F-7$F1F+7&F37$F1$\"++
+++=F/7$$\"#:F*F67$F9F+-%&COLORG6&%$RGBG$\"\"(F*F@$\"#5F*-%'CURVESG6$7
S7$$!3++++++++]!#=$\"#?F+7$$!3pmmm;p0kXFKFL7$$!3JLL$3<XZ=%FKFL7$$!3nmm
mT%p\"ePFKFL7$$!3rmmm\"4m(GLFKFL7$$!3\"QLL3i.9!HFKFL7$$!3\"ommT!R=0DFK
FL7$$!3K++]P8#\\4#FKFL7$$!3*pmmT?F1n\"FKFL7$$!3\\++](y$pZ7FKFL7$$!3vIL
LLyaE\")!#>FL7$$!39mmm;>s%H%FfoFL7$$\"3::'******\\1!>!#@FL7$$\"3p)****
**\\Z/N%FfoFL7$$\"3\\*******\\$fC&)FfoFL7$$\"3ELL$ez6:B\"FKFL7$$\"3Rmm
m;=C#o\"FKFL7$$\"3-mmmm#pS1#FKFL7$$\"3]****\\i`A3DFKFL7$$\"3slmmm(y8!H
FKFL7$$\"3V++]i.tKLFKFL7$$\"39++](3zMu$FKFL7$$\"3\"pmm;H_?<%FKFL7$$\"3
dmm;zihlXFKFL7$$\"3;LLL3#G,*\\FKFL7$$\"3pJL$ezw5V&FKFL7$$\"3(*)***\\PQ
#\\\"eFKFL7$$\"3GKLLe\"*[HiFKFL7$$\"3I*******pvxl'FKFL7$$\"3$z****\\_q
n2(FKFL7$$\"3V)***\\i&p@[(FKFL7$$\"3B)****\\2'HKzFKFL7$$\"3ElmmmZvO$)F
KFL7$$\"3h******\\2go()FKFL7$$\"3UKL$eR<*f\"*FKFL7$$\"3m******\\)Hxe*F
KFL7$$\"3ckm;H!o-***FKFL7$$\"3))***\\7k.6/\"!#<FL7$$\"3emmmT9C#3\"FitF
L7$$\"3\"****\\i!*3`7\"FitFL7$$\"3QLLL$*zym6FitFL7$$\"3GLL$3N1#47FitFL
7$$\"3kmm\"HYt7D\"FitFL7$$\"3&*******p(G**G\"FitFL7$$\"3lmm;9@BM8FitFL
7$$\"3ELLL`v&QP\"FitFL7$$\"30++DOl5;9FitFL7$$\"3/++v.Uac9FitFL7$$\"3++
++++++:FitFL-%'COLOURG6&F?FB$F+F+F^w-%+AXESLABELSG6$%!GFbw-%*AXESTICKS
G6$7$/$\"\"\"!\"%F+/FiwFiw7#FM-%%VIEWG6$;$!+++++q!#5$\"+++++<!\"*%(DEF
AULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve \+
1" "Curve 2" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 24 "La variable \"c
hangement\"" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "d\351finition " }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "lj:= [seq(`if`(li1[k]=li1[k+1],1,0)
, k=1..nn-1)];\nmm:= add(k,k=lj)/(s1);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%#ljG7I\"\"\"\"\"!F'F'F&F'F&F'F&F'F'F&F'F&F&F&F&F'F'F&F'F&F&F&F
'F'F'F'F&F'F'F&F'F&F&F&F&F'F'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#mm
G$\"+s[zr[!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "test" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 64 "esp,var:= mu, sigma2/(nn-1.);\nvaleur_r\351d
uite=(mm-esp)/sqrt(var);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6$%$espG%
$varG6$#\"\"\"\"\"#$\"+5kD5k!#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%/
valeur_r|dyduiteG$!+O:G,;!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 69 "tallyinto(lj, [-0.5..0.5, 0.5..1.5]); \ndisplay(histogram(%), au
tres);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7$-%'WeightG6$;$!\"&!\"\"$\"
\"&F*\"#?-F%6$;F+$\"#:F*\"#>" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 
300 {PLOTDATA 2 "6'-%)POLYGONSG6%7&7$$!\"&!\"\"\"\"!7$F($\"+++++?!\")7
$$\"\"&F*F-7$F1F+7&F37$F1$\"+++++>F/7$$\"#:F*F67$F9F+-%&COLORG6&%$RGBG
$\"\"(F*F@$\"#5F*-%'CURVESG6$7S7$$!3++++++++]!#=$\"#?F+7$$!3pmmm;p0kXF
KFL7$$!3JLL$3<XZ=%FKFL7$$!3nmmmT%p\"ePFKFL7$$!3rmmm\"4m(GLFKFL7$$!3\"Q
LL3i.9!HFKFL7$$!3\"ommT!R=0DFKFL7$$!3K++]P8#\\4#FKFL7$$!3*pmmT?F1n\"FK
FL7$$!3\\++](y$pZ7FKFL7$$!3vILLLyaE\")!#>FL7$$!39mmm;>s%H%FfoFL7$$\"3:
:'******\\1!>!#@FL7$$\"3p)******\\Z/N%FfoFL7$$\"3\\*******\\$fC&)FfoFL
7$$\"3ELL$ez6:B\"FKFL7$$\"3Rmmm;=C#o\"FKFL7$$\"3-mmmm#pS1#FKFL7$$\"3]*
***\\i`A3DFKFL7$$\"3slmmm(y8!HFKFL7$$\"3V++]i.tKLFKFL7$$\"39++](3zMu$F
KFL7$$\"3\"pmm;H_?<%FKFL7$$\"3dmm;zihlXFKFL7$$\"3;LLL3#G,*\\FKFL7$$\"3
pJL$ezw5V&FKFL7$$\"3(*)***\\PQ#\\\"eFKFL7$$\"3GKLLe\"*[HiFKFL7$$\"3I**
*****pvxl'FKFL7$$\"3$z****\\_qn2(FKFL7$$\"3V)***\\i&p@[(FKFL7$$\"3B)**
**\\2'HKzFKFL7$$\"3ElmmmZvO$)FKFL7$$\"3h******\\2go()FKFL7$$\"3UKL$eR<
*f\"*FKFL7$$\"3m******\\)Hxe*FKFL7$$\"3ckm;H!o-***FKFL7$$\"3))***\\7k.
6/\"!#<FL7$$\"3emmmT9C#3\"FitFL7$$\"3\"****\\i!*3`7\"FitFL7$$\"3QLLL$*
zym6FitFL7$$\"3GLL$3N1#47FitFL7$$\"3kmm\"HYt7D\"FitFL7$$\"3&*******p(G
**G\"FitFL7$$\"3lmm;9@BM8FitFL7$$\"3ELLL`v&QP\"FitFL7$$\"30++DOl5;9Fit
FL7$$\"3/++v.Uac9FitFL7$$\"3++++++++:FitFL-%'COLOURG6&F?FB$F+F+F^w-%+A
XESLABELSG6$%!GFbw-%*AXESTICKSG6$7$/$\"\"\"!\"%F+/FiwFiw7#FM-%%VIEWG6$
;$!+++++q!#5$\"+++++<!\"*%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 "
" {TEXT -1 11 "d\351finition " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "lj
:= [seq(`if`(li2[k]=li2[k+1],1,0), k=1..nn-1)];\nmm:= add(k,k=lj)/(s1)
;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ljG7I\"\"\"F&F&F&F&F&\"\"!F&F&
F'F'F&F&F&F'F'F&F&F&F&F&F&F&F&F&F'F&F&F&F&F&F&F'F'F&F&F&F&F&" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#mmG$\"+\\zr[z!#5" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 4 "test" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "esp,var:= mu
, sigma2/(nn-1.);\nvaleur_r\351duite=(mm-esp)/sqrt(var);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>6$%$espG%$varG6$#\"\"\"\"\"#$\"+5kD5k!#7" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#/%/valeur_r|dyduiteG$\"+Qv%Ho$!\"*" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "tallyinto(lj, [-0.5..0.5, 0
.5..1.5]); \ndisplay(histogram(%), autres);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#7$-%'WeightG6$;$!\"&!\"\"$\"\"&F*\"\")-F%6$;F+$\"#:F*\"
#J" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%)POLYGON
SG6%7&7$$!\"&!\"\"\"\"!7$F($\"+++++!)!\"*7$$\"\"&F*F-7$F1F+7&F37$F1$\"
+++++J!\")7$$\"#:F*F67$F:F+-%&COLORG6&%$RGBG$\"\"(F*FA$\"#5F*-%'CURVES
G6$7S7$$!3++++++++]!#=$\"#?F+7$$!3pmmm;p0kXFLFM7$$!3JLL$3<XZ=%FLFM7$$!
3nmmmT%p\"ePFLFM7$$!3rmmm\"4m(GLFLFM7$$!3\"QLL3i.9!HFLFM7$$!3\"ommT!R=
0DFLFM7$$!3K++]P8#\\4#FLFM7$$!3*pmmT?F1n\"FLFM7$$!3\\++](y$pZ7FLFM7$$!
3vILLLyaE\")!#>FM7$$!39mmm;>s%H%FgoFM7$$\"3::'******\\1!>!#@FM7$$\"3p)
******\\Z/N%FgoFM7$$\"3\\*******\\$fC&)FgoFM7$$\"3ELL$ez6:B\"FLFM7$$\"
3Rmmm;=C#o\"FLFM7$$\"3-mmmm#pS1#FLFM7$$\"3]****\\i`A3DFLFM7$$\"3slmmm(
y8!HFLFM7$$\"3V++]i.tKLFLFM7$$\"39++](3zMu$FLFM7$$\"3\"pmm;H_?<%FLFM7$
$\"3dmm;zihlXFLFM7$$\"3;LLL3#G,*\\FLFM7$$\"3pJL$ezw5V&FLFM7$$\"3(*)***
\\PQ#\\\"eFLFM7$$\"3GKLLe\"*[HiFLFM7$$\"3I*******pvxl'FLFM7$$\"3$z****
\\_qn2(FLFM7$$\"3V)***\\i&p@[(FLFM7$$\"3B)****\\2'HKzFLFM7$$\"3ElmmmZv
O$)FLFM7$$\"3h******\\2go()FLFM7$$\"3UKL$eR<*f\"*FLFM7$$\"3m******\\)H
xe*FLFM7$$\"3ckm;H!o-***FLFM7$$\"3))***\\7k.6/\"!#<FM7$$\"3emmmT9C#3\"
FjtFM7$$\"3\"****\\i!*3`7\"FjtFM7$$\"3QLLL$*zym6FjtFM7$$\"3GLL$3N1#47F
jtFM7$$\"3kmm\"HYt7D\"FjtFM7$$\"3&*******p(G**G\"FjtFM7$$\"3lmm;9@BM8F
jtFM7$$\"3ELLL`v&QP\"FjtFM7$$\"30++DOl5;9FjtFM7$$\"3/++v.Uac9FjtFM7$$
\"3++++++++:FjtFM-%'COLOURG6&F@FC$F+F+F_w-%+AXESLABELSG6$%!GFcw-%*AXES
TICKSG6$7$/$\"\"\"!\"%F+/FjwFjw7#FN-%%VIEWG6$;$!+++++q!#5$\"+++++<F/%(
DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Cur
ve 1" "Curve 2" }}}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 24 "Lancer d'un \+
d\351 \351quilibr\351" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "nn:
=120; ra:= 1+rand(6): " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#nnG\"$?\"
" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }{MPLTEXT 0 21 67 "li \+
:= [1, 2, 5, 1, 6, 6, 1, 5, 2, 2, 4, 1, 4, 4, 4, 4, 4, 5, 5, 6]:" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "li:= ['ra()'$nn];" }}{PARA 12 "" 1 
"" {XPPMATH 20 "6#>%#liG7dr\"\"%\"\"$F&\"\"'\"\"&F'F(F'\"\"#F*F*F&F&F'
F'F*\"\"\"F&F&F(F+F+F+F*F&F*F+F'F(F'F(F&F'F(F+F(F'F+F&F(F&F'F*F)F+F)F&
F&F*F(F(F+F*F*F&F*F&F&F*F(F+F+F&F&F*F&F+F&F)F'F&F'F&F&F'F(F(F)F(F+F'F*
F*F)F+F)F*F)F(F)F&F&F(F&F(F*F'F*F+F*F&F)F&F(F+F*F(F'F)F+F)F&F*F'F+F)F+
F(F(F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "th\351orie" }}{PARA 0 ">
 " 0 "" {MPLTEXT 1 0 95 "mu:=add(k*(1/6), k=1..6);\nsigma2:= add((k-mu
)^2*(1/6),k=1..6);\nM4:= add((k-mu)^4*(1/6),k=1..6);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%#muG#\"\"(\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%'sigma2G#\"#N\"#7" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#M4G#\"$2(\"
#[" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "test de m_e" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 85 "m_e:= add(k, k=li)/nn; \nesp,var:= mu, sigma2/
nn; \nz_m:= evalf((m_e-(esp))/sqrt(var));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$m_eG#\"\"(\"\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
6$%$espG%$varG6$#\"\"(\"\"##F)\"$)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%$z_mG$\"\"!F&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "test de v_e \+
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "add(k^2, k=li)/nn-m_e^2*1.;\nv_
e:= %*nn/(nn-1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "esp,var:= (sigm
a2), (M4-(nn-3)/(nn-1)*sigma2^2)/nn;\nz_v:= evalf((v_e-(esp))/sqrt(var
)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*LLL$G!\")" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%$v_eG$\"+aG9dG!\"*" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>6$%$espG%$varG6$#\"#N\"#7#\"%(f#\"&g*[" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$z_vG$!+uO\\%e#!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 
-1 32 "\351valuation de l'auto-corr\351lation" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 153 "s1, sx, sxx, sy, syy, sxy :=nn-1. ,\nadd(li[k],k=1..
nn-1), add(li[k]^2,k=1..nn-1),\nadd(li[k],k=2..nn), add(li[k]^2,k=2..n
n),\nadd(li[k]*li[k+1],k=1..nn-1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
115 "mx:=sx/s1; my:=sy/s1; vx:=sxx/s1-mx^2; vy:=syy/s1-my^2;\ncov:= sx
y/s1-mx*my; rr:= cov/sqrt(vx*vy); frv:= 1/(1-rr^2);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#>6(%#s1G%#sxG%$sxxG%#syG%$syyG%$sxyG6($\"$>\"\"\"!\"$
:%\"%&y\"\"$;%\"%%z\"\"%R9" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#mxG$
\"+e\\R([$!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#myG$\"+>$)z&\\$!
\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vxG$\"*Tw!QG!\")" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%#vyG$\"*OC]&G!\")" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$covG$!(Y#z)*!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#
>%#rrG$!+r#=1Z$!#6" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$frvG$\"+sf?,5
!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "autres:= plot(nn/6,
x=0.5..6.5), tickmarks=[[$1..6], [nn/6]], labels=[``,``]:" }}{PARA 0 "
> " 0 "" {MPLTEXT 1 0 38 "cases:= [seq(k-0.5 .. k+0.5, k=1..6)];" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&casesG7(;$\"\"&!\"\"$\"#:F);F*$\"#D
F);F-$\"#NF);F0$\"#XF);F3$\"#bF);F6$\"#lF)" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 52 "tallyinto(li, cases): display(histogram(%), autres)
;" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%)POLYGONS
G6)7&7$$\"\"&!\"\"\"\"!7$F($\"+++++>!\")7$$\"#:F*F-7$F1F+7&F37$F1$\"++
+++@F/7$$\"#DF*F67$F9F+7&F;7$F9$\"+++++<F/7$$\"#NF*F>7$FAF+7&FC7$FA$\"
+++++GF/7$$\"#XF*FF7$FIF+7&FK7$FI$\"+++++9F/7$$\"#bF*FN7$FQF+7&FS7$FQF
67$$\"#lF*F67$FWF+-%&COLORG6&%$RGBG$\"\"(F*Fhn$\"#5F*-%'CURVESG6$7S7$$
\"3++++++++]!#=$\"#?F+7$$\"3%*******\\#HyI'FcoFdo7$$\"3`****\\([kdW(Fc
oFdo7$$\"3++++v;\\D()FcoFdo7$$\"3;++]s,P,5!#<Fdo7$$\"33++v8*y&H6FbpFdo
7$$\"3&)***\\(G[W[7FbpFdo7$$\"32++v)fB:P\"FbpFdo7$$\"3-++vQ=\"))\\\"Fb
pFdo7$$\"3(****\\P'=pD;FbpFdo7$$\"33+++lN?c<FbpFdo7$$\"3,++]U$e6(=FbpF
do7$$\"3))*****\\>q0+#FbpFdo7$$\"3=+++DM^I@FbpFdo7$$\"3))*****\\!ytbAF
bpFdo7$$\"3?++vQNXpBFbpFdo7$$\"3.+++XDn/DFbpFdo7$$\"3.+++!y?#>EFbpFdo7
$$\"3'****\\(3wY_FFbpFdo7$$\"3#)******HOTqGFbpFdo7$$\"39++v3\">)**HFbp
Fdo7$$\"3:++DEP/BJFbpFdo7$$\"3>++](o:;D$FbpFdo7$$\"3>++v$)[opLFbpFdo7$
$\"3'*****\\i%Qq\\$FbpFdo7$$\"3&****\\(QIKHOFbpFdo7$$\"3#****\\7:xWu$F
bpFdo7$$\"37++]Zn%)oQFbpFdo7$$\"3!)******4FL(*RFbpFdo7$$\"3#)****\\d6.
BTFbpFdo7$$\"3)****\\(o3lWUFbpFdo7$$\"3N++]A))ozVFbpFdo7$$\"3e******Hk
-,XFbpFdo7$$\"36+++D-eIYFbpFdo7$$\"3t***\\(=_(zu%FbpFdo7$$\"3M+++b*=j(
[FbpFdo7$$\"3g***\\(3/3(*\\FbpFdo7$$\"33++vB4JB^FbpFdo7$$\"3v*****\\KC
nC&FbpFdo7$$\"3s***\\(=n#fP&FbpFdo7$$\"3P+++!)RO+bFbpFdo7$$\"30++]_!>w
i&FbpFdo7$$\"3N++v)Q?Qv&FbpFdo7$$\"3G+++5jypeFbpFdo7$$\"3<++]Ujp-gFbpF
do7$$\"3++++gEd@hFbpFdo7$$\"3:++v3'>$[iFbpFdo7$$\"38++D6EjpjFbpFdo7$$
\"3++++++++lFbpFdo-%'COLOURG6&FgnFjn$F+F+Fjx-%+AXESLABELSG6$%!GF^y-%*A
XESTICKSG6$7(\"\"\"\"\"#\"\"$\"\"%F)\"\"'7#Feo-%%VIEWG6$;$!+++++5!#5$
\"+++++r!\"*%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 39 "La variable
 \"diff\351rence\" (d\351 \351quilibr\351)" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 36 "lj:= [seq(li[j+1]-li[j],j=1..nn-1)];" }}{PARA 12 "
" 1 "" {XPPMATH 20 "6#>%#ljG7cr!\"\"\"\"\"\"\"#F&!\"#\"\"$!\"$F&\"\"!F
,F(F,F&F,F&F&F*F,F(!\"&F,F,F'F(F)F&F(F*F+F*F)F&F*F-\"\"&F+F)F*F(F)F&F&
F*!\"%\"\"%F&F,F)F0F,F-F'F,F(F)F(F,F)F0F-F,F*F,F)F(F+F*F'F)F'F&F'F,F&F
*F,F&F'F-F(F&F,F*F/F0F+F*F'F&F&F,F(F)F(F/F'F&F&F'F(F'F&F(F-F'F0F+F(F/F
0F&F)F'F)F0F/F.F,F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "s1,s
x,sxx:= nn-1, add(k,k=lj), add(k^2,k=lj);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>6%%#s1G%#sxG%$sxxG6%\"$>\"\"\"\"\"$,(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "diff_moy:= sx/s1;" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#>%)diff_moyG#\"\"\"\"$>\"" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 72 "esp,var:= 0,2*sigma2/s1;\ndiff_moy_red = evalf((di
ff_moy-esp)/sqrt(var));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6$%$espG%$
varG6$\"\"!#\"\"&\"$-\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%-diff_moy
_redG$\"+nB\\&z$!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "ta_e
x:= tallyinto(lj, [seq(k-0.5 .. k+0.5, k=-5..5)]); pl_ex:= histogram(%
): %;" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%&ta_exG7--%'WeightG6$;$!#b!
\"\"$!#XF,\"\"'-F'6$;F-$!#NF,\"\"&-F'6$;F3$!#DF,F/-F'6$;F9$!#:F,\"#8-F
'6$;F>$!\"&F,\"#A-F'6$;FD$F5F,\"#=-F'6$;FJ$\"#:F,F@-F'6$;FO$\"#DF,FP-F
'6$;FT$\"#NF,\"#7-F'6$;FY$\"#XF,\"\"(-F'6$;Fin$\"#bF,\"\"#" }}{PARA 
13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%)POLYGONSG6-7&7$$!#b
!\"\"\"\"!7$F($\"+++++g!\"*7$$!#XF*F-7$F1F+7&F37$F1$\"+++++]F/7$$!#NF*
F67$F9F+7&F;7$F9F-7$$!#DF*F-7$F?F+7&FA7$F?$\"+++++8!\")7$$!#:F*FD7$FHF
+7&FJ7$FH$\"+++++AFF7$$!\"&F*FM7$FPF+7&FR7$FP$\"+++++=FF7$$\"\"&F*FU7$
FXF+7&FZ7$FXFD7$$\"#:F*FD7$FhnF+7&Fjn7$Fhn$\"+++++:FF7$$\"#DF*F]o7$F`o
F+7&Fbo7$F`o$\"+++++7FF7$$\"#NF*Feo7$FhoF+7&Fjo7$Fho$\"+++++qF/7$$\"#X
F*F]p7$F`pF+7&Fbp7$F`p$\"+++++?F/7$$\"#bF*Fep7$FhpF+-%&COLORG6&%$RGBG$
\"\"(F*F_q$\"#5F*-%%VIEWG6$;$!+++++mF/$\"+++++mF/%(DEFAULTG" 1 2 0 1 
10 0 2 6 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 130 "[seq(Weight(k-.5 .. k+.5, 6-abs(k)
), k=-5..5)];\ndescribe[count](%);\nta_th:= [seq(Weight(k-.5 .. k+.5, \+
(6-abs(k))*nn/%), k=-5..5)]:" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#7--%'W
eightG6$;$!#b!\"\"$!#XF*\"\"\"-F%6$;F+$!#NF*\"\"#-F%6$;F1$!#DF*\"\"$-F
%6$;F7$!#:F*\"\"%-F%6$;F=$!\"&F*\"\"&-F%6$;FC$FEF*\"\"'-F%6$;FI$\"#:F*
FE-F%6$;FN$\"#DF*F?-F%6$;FS$\"#NF*F9-F%6$;FX$\"#XF*F3-F%6$;Fgn$\"#bF*F
-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#O" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 50 "histogram(ta_th, color=yellow): display(pl_ex, %);
" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%)POLYGONSG
6.7&7$$!#b!\"\"\"\"!7$F($\"+++++g!\"*7$$!#XF*F-7$F1F+7&F37$F1$\"+++++]
F/7$$!#NF*F67$F9F+7&F;7$F9F-7$$!#DF*F-7$F?F+7&FA7$F?$\"+++++8!\")7$$!#
:F*FD7$FHF+7&FJ7$FH$\"+++++AFF7$$!\"&F*FM7$FPF+7&FR7$FP$\"+++++=FF7$$
\"\"&F*FU7$FXF+7&FZ7$FXFD7$$\"#:F*FD7$FhnF+7&Fjn7$Fhn$\"+++++:FF7$$\"#
DF*F]o7$F`oF+7&Fbo7$F`o$\"+++++7FF7$$\"#NF*Feo7$FhoF+7&Fjo7$Fho$\"++++
+qF/7$$\"#XF*F]p7$F`pF+7&Fbp7$F`p$\"+++++?F/7$$\"#bF*Fep7$FhpF+-%&COLO
RG6&%$RGBG$\"\"(F*F_q$\"#5F*-F$6.7&F'7$F($\"+LLLLLF/7$F1FgqF37&F37$F1$
\"+nmmmmF/7$F9F\\rF;7&F;7$F9$\"+++++5FF7$F?FarFA7&FA7$F?$\"+LLLL8FF7$F
HFfrFJ7&FJ7$FH$\"+nmmm;FF7$FPF[sFR7&FR7$FP$FfpFF7$FXF`sFZ7&FZ7$FXF[s7$
FhnF[sFjn7&Fjn7$FhnFfr7$F`oFfrFbo7&Fbo7$F`oFar7$FhoFarFjo7&Fjo7$FhoF\\
r7$F`pF\\rFbp7&Fbp7$F`pFgq7$FhpFgqFjp-%'COLOURG6&F^q$\"*++++\"FFFdt$F+
F+-%%VIEWG6$;$!+++++mF/$\"+++++mF/%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 50 "ma:= matrix([map2(op,2,ta_ex), map2(op,2,
ta_th)]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#maG-%'matrixG6#7$7-\"
\"'\"\"&F*\"#8\"#A\"#=F,\"#:\"#7\"\"(\"\"#7-#\"#5\"\"$#\"#?F6F5#\"#SF6
#\"#]F6F8F;F9F5F7F4" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "chi:
= add((ma[1,k]-ma[2,k])^2/ma[2,k], k=1..linalg[coldim](ma));\nnu:= lin
alg[coldim](ma)-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$chiG#\"$.)\"$
+\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#nuG\"#5" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 29 "evalf( (chi-nu)/sqrt(2*nu) );" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#$!+<R00W!#5" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 23 "Lancer d'un
 d\351 b\351gayant" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 120 "rb:= \+
proc() global mrdb; \nif not assigned(mrdb) then mrdb:= ra() fi;\nif r
a()<6 then mrdb:= ra(); fi; \nreturn mrdb;\nend: " }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 17 "li:= ['rb()'$nn];" }}{PARA 12 "" 1 "" 
{XPPMATH 20 "6#>%#liG7dr\"\"%\"\"$F'\"\"&F'\"\"\"F)F&F(F(F(F&F&F'F(F(F
'F&F&F)F&\"\"'F*F*F&\"\"#F+F*F&F*F*F'F*F(F'F&F+F*F)F&F+F)F*F*F+F&F)F'F
'F&F+F&F&F+F)F(F*F*F'F'F'F+F&F'F&F*F+F(F(F'F*F'F'F*F*F'F&F*F&F(F(F(F&F
+F(F+F*F*F*F+F)F)F)F(F+F+F(F*F(F'F'F'F'F*F(F*F'F)F'F'F)F*F&F&F(F&F&F&F
+F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 11 "test de m_e" }}{PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 85 "m_e:= add(k, k=li)/nn; \nesp,var:= mu, sigma2/
nn; \nz_m:= evalf((m_e-(esp))/sqrt(var));" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$m_eG#\"#\"*\"#C" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>
6$%$espG%$varG6$#\"\"(\"\"##F)\"$)G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%$z_mG$\"+%pG3(=!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "test de
 v_e " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "add(k^2, k=li)/nn-m_e^2*1.
;\nv_e:= %*nn/(nn-1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "esp,var:= \+
(sigma2), (M4-(nn-3)/(nn-1)*sigma2^2)/nn;\nz_v:= evalf((v_e-(esp))/sqr
t(var)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"**QE[D!\")" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%$v_eG$\"+synpD!\"*" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>6$%$espG%$varG6$#\"#N\"#7#\"%(f#\"&g*[" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>%$z_vG$!+#p2m]\"!\"*" }}}{EXCHG {PARA 0 "" 0 "" 
{TEXT -1 32 "\351valuation de l'auto-corr\351lation" }}{PARA 0 "> " 0 
"" {MPLTEXT 1 0 153 "s1, sx, sxx, sy, syy, sxy :=nn-1. ,\nadd(li[k],k=
1..nn-1), add(li[k]^2,k=1..nn-1),\nadd(li[k],k=2..nn), add(li[k]^2,k=2
..nn),\nadd(li[k]*li[k+1],k=1..nn-1);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 
0 115 "mx:=sx/s1; my:=sy/s1; vx:=sxx/s1-mx^2; vy:=syy/s1-my^2;\ncov:= \+
sxy/s1-mx*my; rr:= cov/sqrt(vx*vy); frv:= 1/(1-rr^2);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#>6(%#s1G%#sxG%$sxxG%#syG%$syyG%$sxyG6($\"$>\"\"\"!
\"$`%\"%F?\"$^%\"%:?\"%i<" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#mxG$\"
+*oAn!Q!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#myG$\"+mf\"**y$!\"*
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#vxG$\"*#eZUD!\")" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%#vyG$\"*35$pD!\")" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#>%$covG$\")fj&z$!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%#rrG$\"+IK2&[\"!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$frvG$\"+#z
^D-\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "autres:= plot(
nn/6,x=0.5..6.5), tickmarks=[[$1..6], [nn/6]], labels=[``,``]:" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "cases:= [seq(k-0.5 .. k+0.5, k=1..6
)];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&casesG7(;$\"\"&!\"\"$\"#:F);
F*$\"#DF);F-$\"#NF);F0$\"#XF);F3$\"#bF);F6$\"#lF)" }}}{EXCHG {PARA 0 "
> " 0 "" {MPLTEXT 1 0 52 "tallyinto(li, cases): display(histogram(%), \+
autres);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%)P
OLYGONSG6)7&7$$\"\"&!\"\"\"\"!7$F($\"+++++7!\")7$$\"#:F*F-7$F1F+7&F37$
F1$\"+++++;F/7$$\"#DF*F67$F9F+7&F;7$F9$\"+++++CF/7$$\"#NF*F>7$FAF+7&FC
7$FA$\"+++++DF/7$$\"#XF*FF7$FIF+7&FK7$FI$\"+++++>F/7$$\"#bF*FN7$FQF+7&
FS7$FQF>7$$\"#lF*F>7$FWF+-%&COLORG6&%$RGBG$\"\"(F*Fhn$\"#5F*-%'CURVESG
6$7S7$$\"3++++++++]!#=$\"#?F+7$$\"3%*******\\#HyI'FcoFdo7$$\"3`****\\(
[kdW(FcoFdo7$$\"3++++v;\\D()FcoFdo7$$\"3;++]s,P,5!#<Fdo7$$\"33++v8*y&H
6FbpFdo7$$\"3&)***\\(G[W[7FbpFdo7$$\"32++v)fB:P\"FbpFdo7$$\"3-++vQ=\")
)\\\"FbpFdo7$$\"3(****\\P'=pD;FbpFdo7$$\"33+++lN?c<FbpFdo7$$\"3,++]U$e
6(=FbpFdo7$$\"3))*****\\>q0+#FbpFdo7$$\"3=+++DM^I@FbpFdo7$$\"3))*****
\\!ytbAFbpFdo7$$\"3?++vQNXpBFbpFdo7$$\"3.+++XDn/DFbpFdo7$$\"3.+++!y?#>
EFbpFdo7$$\"3'****\\(3wY_FFbpFdo7$$\"3#)******HOTqGFbpFdo7$$\"39++v3\"
>)**HFbpFdo7$$\"3:++DEP/BJFbpFdo7$$\"3>++](o:;D$FbpFdo7$$\"3>++v$)[opL
FbpFdo7$$\"3'*****\\i%Qq\\$FbpFdo7$$\"3&****\\(QIKHOFbpFdo7$$\"3#****
\\7:xWu$FbpFdo7$$\"37++]Zn%)oQFbpFdo7$$\"3!)******4FL(*RFbpFdo7$$\"3#)
****\\d6.BTFbpFdo7$$\"3)****\\(o3lWUFbpFdo7$$\"3N++]A))ozVFbpFdo7$$\"3
e******Hk-,XFbpFdo7$$\"36+++D-eIYFbpFdo7$$\"3t***\\(=_(zu%FbpFdo7$$\"3
M+++b*=j([FbpFdo7$$\"3g***\\(3/3(*\\FbpFdo7$$\"33++vB4JB^FbpFdo7$$\"3v
*****\\KCnC&FbpFdo7$$\"3s***\\(=n#fP&FbpFdo7$$\"3P+++!)RO+bFbpFdo7$$\"
30++]_!>wi&FbpFdo7$$\"3N++v)Q?Qv&FbpFdo7$$\"3G+++5jypeFbpFdo7$$\"3<++]
Ujp-gFbpFdo7$$\"3++++gEd@hFbpFdo7$$\"3:++v3'>$[iFbpFdo7$$\"38++D6EjpjF
bpFdo7$$\"3++++++++lFbpFdo-%'COLOURG6&FgnFjn$F+F+Fjx-%+AXESLABELSG6$%!
GF^y-%*AXESTICKSG6$7(\"\"\"\"\"#\"\"$\"\"%F)\"\"'7#Feo-%%VIEWG6$;$!+++
++5!#5$\"+++++r!\"*%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 
45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 0 "" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 38 "La varia
ble \"diff\351rence\" (d\351 b\351gayant)" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 36 "lj:= [seq(li[j+1]-li[j],j=1..nn-1)];" }}{PARA 12 "" 
1 "" {XPPMATH 20 "6#>%#ljG7cr!\"\"\"\"!\"\"#!\"#F)F'\"\"$\"\"\"F'F'F&F
'F&F(F'F)F+F'!\"$F*F(F'F'F)F)F'\"\"%F)F(F'F,F*F&F)F+F)F-!\"&F*F)F&\"\"
&F'!\"%F(F,F(F'F+F)F(F'F)F&F-F+F'F,F'F'F&F(F&F+F(F0F*F'F)F*F,F'F*F'F,F
+F(F)F+F'F'F&F)F*F,F-F'F'F0F&F'F'F-F,F'F*F+F&F)F'F'F'F*F&F+F,F)F(F'F)F
/F)F'F+F&F'F'F)F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "s1,sx,
sxx:= nn-1, add(k,k=lj), add(k^2,k=lj);" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>6%%#s1G%#sxG%$sxxG6%\"$>\"!\"#\"$=&" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 17 "diff_moy:= sx/s1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#>%)diff_moyG#!\"#\"$>\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
72 "esp,var:= 0,2*sigma2/s1;\ndiff_moy_red = evalf((diff_moy-esp)/sqrt
(var));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>6$%$espG%$varG6$\"\"!#\"\"
&\"$-\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/%-diff_moy_redG$!+LZ)4f(!#
6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "ta_ex:= tallyinto(lj, \+
[seq(k-0.5 .. k+0.5, k=-5..5)]); pl_ex:= histogram(%): %;" }}{PARA 12 
"" 1 "" {XPPMATH 20 "6#>%&ta_exG7--%'WeightG6$;$!#b!\"\"$!#XF,\"\"\"-F
'6$;F-$!#NF,\"\"$-F'6$;F3$!#DF,\"\"*-F'6$;F9$!#:F,\"#>-F'6$;F?$!\"&F,
\"#8-F'6$;FE$\"\"&F,\"#N-F'6$;FK$\"#:F,\"#6-F'6$;FQ$\"#DF,FS-F'6$;FW$F
MF,\"#5-F'6$;Ffn$\"#XF,FL-F'6$;F[o$\"#bF,\"\"#" }}{PARA 13 "" 1 "" 
{GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%)POLYGONSG6-7&7$$!#b!\"\"\"\"!7
$F($\"+++++5!\"*7$$!#XF*F-7$F1F+7&F37$F1$\"+++++IF/7$$!#NF*F67$F9F+7&F
;7$F9$\"+++++!*F/7$$!#DF*F>7$FAF+7&FC7$FA$\"+++++>!\")7$$!#:F*FF7$FJF+
7&FL7$FJ$\"+++++8FH7$$!\"&F*FO7$FRF+7&FT7$FR$\"+++++NFH7$$\"\"&F*FW7$F
ZF+7&Ffn7$FZ$\"+++++6FH7$$\"#:F*Fin7$F\\oF+7&F^oF[o7$$\"#DF*Fin7$FaoF+
7&Fco7$Fao$F.FH7$$\"#NF*Ffo7$FhoF+7&Fjo7$Fho$\"+++++]F/7$$\"#XF*F]p7$F
`pF+7&Fbp7$F`p$\"+++++?F/7$$\"#bF*Fep7$FhpF+-%&COLORG6&%$RGBG$\"\"(F*F
_q$\"#5F*-%%VIEWG6$;$!+++++mF/$\"+++++mF/%(DEFAULTG" 1 2 0 1 10 0 2 6 
1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 50 "histogram(ta_th, color=yellow): display(pl_ex
, %);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%)POLY
GONSG6.7&7$$!#b!\"\"\"\"!7$F($\"+++++5!\"*7$$!#XF*F-7$F1F+7&F37$F1$\"+
++++IF/7$$!#NF*F67$F9F+7&F;7$F9$\"+++++!*F/7$$!#DF*F>7$FAF+7&FC7$FA$\"
+++++>!\")7$$!#:F*FF7$FJF+7&FL7$FJ$\"+++++8FH7$$!\"&F*FO7$FRF+7&FT7$FR
$\"+++++NFH7$$\"\"&F*FW7$FZF+7&Ffn7$FZ$\"+++++6FH7$$\"#:F*Fin7$F\\oF+7
&F^oF[o7$$\"#DF*Fin7$FaoF+7&Fco7$Fao$F.FH7$$\"#NF*Ffo7$FhoF+7&Fjo7$Fho
$\"+++++]F/7$$\"#XF*F]p7$F`pF+7&Fbp7$F`p$\"+++++?F/7$$\"#bF*Fep7$FhpF+
-%&COLORG6&%$RGBG$\"\"(F*F_q$\"#5F*-F$6.7&F'7$F($\"+LLLLLF/7$F1FgqF37&
F37$F1$\"+nmmmmF/7$F9F\\rF;7&F;7$F9Ffo7$FAFfoFC7&FC7$FA$\"+LLLL8FH7$FJ
FdrFL7&FL7$FJ$\"+nmmm;FH7$FRFirFT7&FT7$FR$FfpFH7$FZF^sFfn7&Ffn7$FZFir7
$F\\oFirF^o7&F^o7$F\\oFdr7$FaoFdrFcoFdo7&Fjo7$FhoF\\r7$F`pF\\rFbp7&Fbp
7$F`pFgq7$FhpFgqFjp-%'COLOURG6&F^q$\"*++++\"FHF_t$F+F+-%%VIEWG6$;$!+++
++mF/$\"+++++mF/%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 50 "ma:= matrix([map2(op,2,ta_ex), map2(op,2,ta_th)]);" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#maG-%'matrixG6#7$7-\"\"\"\"\"$\"\"
*\"#>\"#8\"#N\"#6F0\"#5\"\"&\"\"#7-#F1F+#\"#?F+F1#\"#SF+#\"#]F+F7F:F8F
1F6F5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 98 "chi:= evalf(add((m
a[1,k]-ma[2,k])^2/ma[2,k], k=1..linalg[coldim](ma)));\nnu:= linalg[col
dim](ma)-1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$chiG$\"++++]@!\")" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#nuG\"#5" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 29 "evalf( (chi-nu)/sqrt(2*nu) );" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"+v\"y9d#!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 14 "Chi2(nu, chi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+HTN@)*!#
5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "plot(chi2(nu,t), t=0..
30);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVE
SG6$7_o7$$\"\"!F)F(7$$\"3')*****\\7t&pK!#=$\"3QxU@>pej7!#A7$$\"3s*****
*\\i9RlF-$\"3/^4zJ(Hor\"!#@7$$\"3[**\\(oHl:'zF-$\"3io%>OkwN^$F67$$\"3M
++vVV)RQ*F-$\"3aHq%>EQcJ'F67$$\"37+D1R.k!3\"!#<$\"3@.b@b-WM5!#?7$$\"3*
****\\PC#)GA\"FD$\"38R1m>\"3*z:FG7$$\"3%***\\iSS\"Ga\"FD$\"3RBrLm&\\4T
$FG7$$\"3*)****\\Peui=FD$\"3VSib#G$zwhFG7$$\"3L+++]$)z%=#FD$\"3PT$G`Fv
3&**FG7$$\"3L++]i3&o]#FD$\"3<a&4:!*R#o9!#>7$$\"39+]i:FPFGFD$\"3#Ru\"Q=
--C?F[o7$$\"3'****\\(oX*y9$FD$\"3ujZ%oe$\\\\EF[o7$$\"3\")***\\iNf]W$FD
$\"3c\">\">mU(fF$F[o7$$\"3o***\\P9CAu$FD$\"3A`^\\1OPJRF[o7$$\"3!)***\\
(o5#*\\SFD$\"3jcc\"*=ewBYF[o7$$\"3#****\\P*zhdVFD$\"3W,VviAi8`F[o7$$\"
3*****\\PfQen%FD$\"3QvNqv+-3gF[o7$$\"33++v$>fS*\\FD$\"3mal+10=omF[o7$$
\"3^++Dc#f7J&FD$\"3R<ws<D`zsF[o7$$\"30++v=$f%GcFD$\"3)3cf`-hT$yF[o7$$
\"3m**\\(=dQZ&fFD$\"3HMl/fYZP$)F[o7$$\"3<+++Dy,\"G'FD$\"3sOM2FT/n()F[o
7$$\"3I++]7<zboFD$\"3.$4wR0JeL*F[o7$$\"3u++vV8KzrFD$\"3Sa\"zpY\")*\\&*
F[o7$$\"3J+++v4&G](FD$\"3NF)RFuI**o*F[o7$$\"3B++]7+GlwFD$\"3*)****zf%=
Kt*F[o7$$\"3G******\\!4x#yFD$\"3#oe'3=9:f(*F[o7$$\"3?****\\(3Q,*zFD$\"
3H0)\\u-6$o(*F[o7$$\"39*****\\7nD:)FD$\"3iHnlcoKh(*F[o7$$\"3q*****\\2G
cY)FD$\"34&[&*)oc#[q*F[o7$$\"3E+++D!*oy()FD$\"3?IU9+,)ff*F[o7$$\"3=+]P
f$yH1*FD$\"3ixy&\\H7jX*F[o7$$\"35++v$pnsM*FD$\"3;>Kf_W0#G*F[o7$$\"3,++
]siL-5!#;$\"3\\8:+L+!Gv)F[o7$$\"3#********Q5'f5Fbv$\"3ZJrB^@N4#)F[o7$$
\"3*)**\\P/QBE6Fbv$\"3SpS,aau3vF[o7$$\"3\"******\\\"o?&=\"Fbv$\"3kEnkE
))edoF[o7$$\"3-+]Pa&4*\\7Fbv$\"3>rE\"=_Zx8'F[o7$$\"3.+]7j=_68Fbv$\"3D$
=V6+MxY&F[o7$$\"3+++vVy!eP\"Fbv$\"3]/$)\\\">/6![F[o7$$\"39+](=WU[V\"Fb
v$\"3w+CKu))*zA%F[o7$$\"31++DJ#>&)\\\"Fbv$\"31Vu@X7VeOF[o7$$\"3)***\\P
>:mk:Fbv$\"3+jlEu$GR7$F[o7$$\"3()**\\iv&QAi\"Fbv$\"3&=d^-4qnq#F[o7$$\"
3:++vtLU%o\"Fbv$\"3tE0Z#)*)\\0BF[o7$$\"3%******\\Nm'[<Fbv$\"3D[Wb\"zj@
%>F[o7$$\"34++vyb^6=Fbv$\"3,GcPY(>Oj\"F[o7$$\"3****\\PMaKs=Fbv$\"38!y2
vh,bP\"F[o7$$\"3#)***\\7TW)R>Fbv$\"3/w0=)3038\"F[o7$$\"3z*****\\@80+#F
bv$\"3[^Cp3iwV%*FG7$$\"3'*****\\7,Hl?Fbv$\"3d2>N#Rd'fxFG7$$\"3')**\\P4
w)R7#Fbv$\"3[x_PLFTskFG7$$\"3N++]x%f\")=#Fbv$\"3Uu-j$\\Z'*G&FG7$$\"3(*
**\\P/-a[AFbv$\"3.]O[\"eB6O%FG7$$\"38+](=Yb;J#Fbv$\"3ykyKhnK`NFG7$$\"3
y****\\i@OtBFbv$\"3[L'[0kU+!HFG7$$\"3/+]PfL'zV#Fbv$\"3qw,Uf#QwL#FG7$$
\"35+++!*>=+DFbv$\"3G,s,58I%*=FG7$$\"3?++DE&4Qc#Fbv$\"3a%z5swUQ_\"FG7$
$\"3<+]P%>5pi#Fbv$\"3!)HWHm!e]A\"FG7$$\"3K+++bJ*[o#Fbv$\"3xEB()fRS+5FG
7$$\"3E++Dr\"[8v#Fbv$\"3S@&*>Fz08zF67$$\"3#)******Hjy5GFbv$\"3$oIX37>L
S'F67$$\"3D+]P/)fT(GFbv$\"3s=`dnVX*4&F67$$\"3:+]i0j\"[$HFbv$\"39![JaG`
M4%F67$$\"#IF)$\"3r$pUl`8jA$F6-%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%+AXESL
ABELSG6$Q\"t6\"Q!6\"-%%VIEWG6$;F(Fa`l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 
2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 26 "plot(Chi2(nu,t), t=0..30);" }}{PARA 13 "" 1 "" 
{GLPLOT2D 400 300 300 {PLOTDATA 2 "6%-%'CURVESG6$7S7$$\"\"!F)F(7$$\"3s
******\\i9Rl!#=$\"3aw-S%QJOP#!#A7$$\"3*****\\PC#)GA\"!#<$\"3/41hcY2&H%
!#@7$$\"3*)****\\Peui=F4$\"3GbzRPp07F!#?7$$\"3L++]i3&o]#F4$\"3a*H_iD*[
C#*F=7$$\"3'****\\(oX*y9$F4$\"3uwa@\"=\"RFA!#>7$$\"3o***\\P9CAu$F4$\"3
())RV-cks<%FH7$$\"3#****\\P*zhdVF4$\"3-%z4`#pVAqFH7$$\"33++v$>fS*\\F4$
\"36UoKM[D%3\"F-7$$\"30++v=$f%GcF4$\"3/R]/NyYX:F-7$$\"3<+++Dy,\"G'F4$
\"3IEp\"e!Rt)3#F-7$$\"3I++]7<zboF4$\"3#*>Yukj95EF-7$$\"3J+++v4&G](F4$
\"3=7ND$3'GFKF-7$$\"39*****\\7nD:)F4$\"3Tz7^FwigQF-7$$\"3E+++D!*oy()F4
$\"3g)H*z'o@xY%F-7$$\"35++v$pnsM*F4$\"3(G1+akf]+&F-7$$\"3,++]siL-5!#;$
\"3FQO))H,a:cF-7$$\"3#********Q5'f5Fhp$\"3qT'RQ7?;5'F-7$$\"3*)**\\P/QB
E6Fhp$\"3vaSzb)=bi'F-7$$\"3\"******\\\"o?&=\"Fhp$\"3\\4&yWN4#\\qF-7$$
\"3-+]Pa&4*\\7Fhp$\"3pb$y'z;fpuF-7$$\"3.+]7j=_68Fhp$\"3,qu-(3!*p#yF-7$
$\"3+++vVy!eP\"Fhp$\"3W!pIFt[o:)F-7$$\"39+](=WU[V\"Fhp$\"3%GcX&3=;B%)F
-7$$\"31++DJ#>&)\\\"Fhp$\"3/CkP([tRn)F-7$$\"3)***\\P>:mk:Fhp$\"3Igkupz
%z*))F-7$$\"3()**\\iv&QAi\"Fhp$\"3*4\"Q!*\\8fl!*F-7$$\"3:++vtLU%o\"Fhp
$\"3lxK,`Y<@#*F-7$$\"3%******\\Nm'[<Fhp$\"3gG*)pcgMd$*F-7$$\"34++vyb^6
=Fhp$\"3p^0&f\"3[p%*F-7$$\"3****\\PMaKs=Fhp$\"3E?@ta7yg&*F-7$$\"3#)***
\\7TW)R>Fhp$\"3HEz(oje^k*F-7$$\"3z*****\\@80+#Fhp$\"3`M0#3;ezq*F-7$$\"
3'*****\\7,Hl?Fhp$\"3z15]Ix^j(*F-7$$\"3')**\\P4w)R7#Fhp$\"3:()yJGQ=0)*
F-7$$\"3N++]x%f\")=#Fhp$\"3fm$>402G%)*F-7$$\"3(***\\P/-a[AFhp$\"3`Y_zD
,'=()*F-7$$\"38+](=Yb;J#Fhp$\"3_o#*3Qcv'*)*F-7$$\"3y****\\i@OtBFhp$\"3
1I^EKGg;**F-7$$\"3/+]PfL'zV#Fhp$\"3A9IX$ofM$**F-7$$\"35+++!*>=+DFhp$\"
34Mk=I%zl%**F-7$$\"3?++DE&4Qc#Fhp$\"3TsZp,MTd**F-7$$\"3<+]P%>5pi#Fhp$
\"3*pKD\\r`g'**F-7$$\"3K+++bJ*[o#Fhp$\"3oY\"pUq%[s**F-7$$\"3E++Dr\"[8v
#Fhp$\"3*Q_@H;7%y**F-7$$\"3#)******Hjy5GFhp$\"3o7Fa%o^E)**F-7$$\"3D+]P
/)fT(GFhp$\"3'f`SZZ\"G')**F-7$$\"3:+]i0j\"[$HFhp$\"3!p5#=h(e!*)**F-7$$
\"#IF)$\"3oYA*yeL9***F--%'COLOURG6&%$RGBG$\"#5!\"\"F(F(-%+AXESLABELSG6
$Q\"t6\"Q!6\"-%%VIEWG6$;F(Fgz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 109 "law:= chi2(n,t); int(law, t=0..infinity);\nint(t*l
aw, t=0..infinity);\nexpand(int(t^2*law, t=0..infinity)-%^2);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$lawG*&*&)%\"tG,&%\"nG#\"\"\"\"\"#F,
!\"\"F,-%$expG6#,$F(#F.F-F,F,*&)F-,$F*F+F,-%&GAMMAG6#F6F,F." }}{PARA 
6 "" 1 "" {TEXT -1 68 "Definite integration: Can't determine if the in
tegral is convergent." }}{PARA 6 "" 1 "" {TEXT -1 34 "Need to know the
 sign of --> 1/2*n" }}{PARA 6 "" 1 "" {TEXT -1 57 "Will now try indefi
nite integration and then take limits." }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#%\"nG" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,$%\"nG\"\"#" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 
-1 22 "Exemple de convolution" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 21 "D
istribution uniforme" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "Heaviside(t
)-Heaviside(t-2); int(%, t=-infinity..+infinity); f:= unapply(%%/%,t);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%*HeavisideG6#%\"tG\"\"\"-F%6#,
&F'F(\"\"#!\"\"F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"#" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"tG6\"6$%)operatorG%&arrowGF(,&-%
*HeavisideG6#9$#\"\"\"\"\"#*&#F2F3F2-F.6#,&F0F2F3!\"\"F2F9F(F(F(" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "Heaviside(t-3)-Heaviside(t-6
): int(%, t=-infinity..+infinity): g:= unapply(%%/%,t);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#>%\"gGR6#%\"tG6\"6$%)operatorG%&arrowGF(,&-%*Hea
visideG6#,&9$\"\"\"\"\"$!\"\"#F2F3*&#F2F3F2-F.6#,&F1F2\"\"'F4F2F4F(F(F
(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "displayg(plot(f(t),t=-
1..3, axes=boxed), tickmarks=[[0,2],[0,0.5]]); " }}{PARA 13 "" 1 "" 
{GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6$7co7$$!\"\"\"\"!$F*F*
7$$!3PLLLLQ6G\"*!#=F+7$$!3hmmmT.\\p$)F/F+7$$!3LLLL$))Qj^(F/F+7$$!3TLLL
$=Kvl'F/F+7$$!3hnmmTs!G!eF/F+7$$!3iLLL3yO5]F/F+7$$!3j+++vE%)*=%F/F+7$$
!3)RLL$3WDTLF/F+7$$!3'4++]d(Q&\\#F/F+7$$!3:mmmm&4`i\"F/F+7$$!3p*****\\
(p7U7F/F+7$$!3GKLLLQW*e)!#>F+7$$!39,++D'zDV'FQF+7$$!3**pmm;arvUFQF+7$$
!3U/+]7LG(>$FQF+7$$!3%)QLL37&)=@FQF+7$$!311+Dc^jz:FQF+7$$!3Ftm;/\">//
\"FQF+7$$!3xo+D\"y5\"3x!#?F+7$$!3$[SL3_I?,&FaoF+7$$!3!4u;/E]fJ#FaoF+7$
$\"3HI#*******H,Q!#@$\"3++++++++]F/7$$\"3%[*******RXpVFQF\\p7$$\"3Q(**
*****\\*3q)FQF\\p7$$\"3!********p=\\q\"F/F\\p7$$\"3^mmm\"fBIY#F/F\\p7$
$\"3yKLLLO[kLF/F\\p7$$\"3.KLLL&Q\"GTF/F\\p7$$\"3+*****\\s]k,&F/F\\p7$$
\"3WJLLLvv-eF/F\\p7$$\"3'3++]sgam'F/F\\p7$$\"3F+++v\"ep[(F/F\\p7$$\"3$
QLLLe/TM)F/F\\p7$$\"39LLLeDBJ\"*F/F\\p7$$\"3Immm;kD!)**F/F\\p7$$\"3Mmm
;f`@'3\"!#<F\\p7$$\"3z****\\nZ)H;\"FhrF\\p7$$\"3YmmmJy*eC\"FhrF\\p7$$
\"3')******R^bJ8FhrF\\p7$$\"3f*****\\5a`T\"FhrF\\p7$$\"3o****\\7RV'\\
\"FhrF\\p7$$\"3l*****\\@fke\"FhrF\\p7$$\"30LLL`4Nn;FhrF\\p7$$\"3#*****
**\\,s`<FhrF\\p7$$\"3[mm;zM)>$=FhrF\\p7$$\"3$*******pfa<>FhrF\\p7$$\"3
Umm\"zy*zd>FhrF\\p7$$\"3#HLLeg`!)*>FhrF\\p7$$\"3Ym\"H#3Mo+?FhrF+7$$\"3
c**\\i5KJ.?FhrF+7$$\"36L3-8I%f+#FhrF+7$$\"3mmmT:Gd3?FhrF+7$$\"3JL$3-UK
Q,#FhrF+7$$\"3'******\\-#4>?FhrF+7$$\"3ELLeM7hH?FhrF+7$$\"3cmm;W/8S?Fh
rF+7$$\"3;LLLj)o61#FhrF+7$$\"3w****\\#G2A3#FhrF+7$$\"3Ymm\"H3XL7#FhrF+
7$$\"3;LLL$)G[k@FhrF+7$$\"3#)****\\7yh]AFhrF+7$$\"3xmmm')fdLBFhrF+7$$
\"3bmmm,FT=CFhrF+7$$\"3FLL$e#pa-DFhrF+7$$\"3*)******Rv&)zDFhrF+7$$\"3H
LLLGUYoEFhrF+7$$\"3_mmm1^rZFFhrF+7$$\"34++]sI@KGFhrF+7$$\"34++]2%)38HF
hrF+7$$\"\"$F*F+-%'COLOURG6&%$RGBG$\"#5F)F+F+-%*AXESSTYLEG6#%$BOXG-%%F
ONTG6%%&TIMESG%&ROMANG\"#;-%+AXESLABELSG6%Q!6\"FbzFiy-%*AXESTICKSG6%7$
F*\"\"#7$F*$\"\"&F)Fiy-%%VIEWG6$;F(F]y%(DEFAULTG" 1 2 0 1 10 0 2 9 1 
2 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 69 "displayg(plot(g(t),t=2..7, axes=boxed), tickma
rks=[[3,6],[0,0.33]]) ;" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 
{PLOTDATA 2 "6(-%'CURVESG6$7co7$$\"\"#\"\"!$F*F*7$$\"3FLL$3x&)*3@!#<F+
7$$\"3\"om\"H2P\"Q?#F/F+7$$\"3RLLeRwX5BF/F+7$$\"3CLL3x%3yT#F/F+7$$\"3m
m;z%4\\Y_#F/F+7$$\"38L$eR-/Pi#F/F+7$$\"3%)**\\il'pis#F/F+7$$\"3>L$e*)>
VB$GF/F+7$$\"3Xm;/w)4_)GF/F+7$$\"3;+]7`l2QHF/F+7$$\"3];a)3\\m_'HF/F+7$
$\"3GLekGkX#*HF/F+7$$\"3g&)e'3<be*HF/F+7$$\"3[Pf38RD**HF/F+7$$\"3N*)fI
bEl-IF/$\"3:LLLLLLLL!#=7$$\"3nTg_(R^g+$F/FZ7$$\"3'e9m>))[G,$F/FZ7$$\"3
1]iSmjk>IF/FZ7$$\"3XekGN8CLIF/FZ7$$\"3%ommTIOo/$F/FZ7$$\"3E+]7GTt%4$F/
FZ7$$\"3oLL3_>jUJF/FZ7$$\"3\"*****\\i^Z]KF/FZ7$$\"3&)****\\(=h(eLF/FZ7
$$\"30++]P[6jMF/FZ7$$\"3lL$e*[z(yb$F/FZ7$$\"3)pmmTXg0n$F/FZ7$$\"3%ommm
J<gw$F/FZ7$$\"3#)**\\iSj0xQF/FZ7$$\"3#omm;pW`(RF/FZ7$$\"3L+]i!f#=$3%F/
FZ7$$\"3v**\\(=xpe=%F/FZ7$$\"3omm\"H28IH%F/FZ7$$\"3?n;zpSS\"R%F/FZ7$$
\"3%GL$3_?`(\\%F/FZ7$$\"3fL$e*)>pxg%F/FZ7$$\"33+]Pf4t.ZF/FZ7$$\"3=MLe*
Gst![F/FZ7$$\"3\\+++DRW9\\F/FZ7$$\"3:++DJE>>]F/FZ7$$\"3F+]i!RU07&F/FZ7
$$\"3+++v=S2L_F/FZ7$$\"3Jmmm\"p)=M`F/FZ7$$\"3B++](=]@W&F/FZ7$$\"36L$e*
[$z*RbF/FZ7$$\"3e++]iC$pk&F/FZ7$$\"3.m;H2qcZdF/FZ7$$\"3!3+DJ5fF&eF/FZ7
$$\"3&Q$ek`8=/fF/FZ7$$\"3!pmmTg.c&fF/FZ7$$\"3ie*[o=i!pfF/FZ7$$\"3M]7`p
2_#)fF/FZ7$$\"3?'Rs31]#*)fF/FZ7$$\"31UN@_$zf*fF/FZ7$$\"3c9T)y*RM**fF/F
Z7$$\"3#zoaNk3F+'F/F+7$$\"3Hh_A*Gtg+'F/F+7$$\"3yLe*[$zV4gF/F+7$$\"3A</
E+^NOgF/F+7$$\"3x**\\ilAFjgF/F+7$$\"3ym\"zW7@^6'F/F+7$$\"3zLLL$)*pp;'F
/F+7$$\"3(RL$3xe,tiF/F+7$$\"3Dn;HdO=yjF/F+7$$\"3a+++D>#[Z'F/F+7$$\"3Sn
mT&G!e&e'F/F+7$$\"3#RLLL)Qk%o'F/F+7$$\"37+]iSjE!z'F/F+7$$\"3c+]P40O\"*
oF/F+7$$\"\"(F*F+-%'COLOURG6&%$RGBG$\"#5!\"\"F+F+-%*AXESSTYLEG6#%$BOXG
-%%FONTG6%%&TIMESG%&ROMANG\"#;-%+AXESLABELSG6%Q!6\"F`zFgy-%*AXESTICKSG
6%7$\"\"$\"\"'7$F*$\"#L!\"#Fgy-%%VIEWG6$;F(Fjx%(DEFAULTG" 1 2 0 1 10 
0 2 9 1 2 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG 
{PARA 0 "" 0 "" {TEXT -1 15 "loi de la somme" }}{PARA 0 "> " 0 "" 
{MPLTEXT 1 0 60 "int(f(t)*g(x-t), t=-infinity..+infinity);\nls:= unapp
ly(%,x):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "displayg(plot(ls(x), x=
2..9, axes=boxed), tickmarks=[[3,5,6,8],[0,0.33]]);" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%$intG6$*&,&-%*HeavisideG6#%\"tG#\"\"\"\"\"#*&#F-F.F
--F)6#,&F+F-F.!\"\"F-F4F-,&-F)6#,(%\"xGF-F+F4\"\"$F4#F-F:*&#F-F:F--F)6
#,(F9F-F+F4\"\"'F4F-F4F-/F+;,$%)infinityGF4FE" }}{PARA 13 "" 1 "" 
{GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6$7]p7$$\"\"#\"\"!$F*F*
7$$\"+z+e_@!\"*F+7$$\"+!>R`G#F/F+7$$\"+&pSYV#F/F+7$$\"+o=$\\e#F/F+7$$
\"+K(3Xt#F/F+7$$\"+#=ZQ!GF/F+7$$\"+Lc=tGF/F+7$$\"+2O34HF/F+7$$\"+#e\")
\\%HF/F+7$$\"+p0$H'HF/F+7$$\"+d&z3)HF/F+7$$\"+]S&)*)HF/F+7$$\"+W&G))*H
F/F+7$$\"+QI!y+$F/$\"+Lj]+8!#77$$\"+Kvx;IF/$\"+L`D'z#FY7$$\"+0!H54$F/$
\"+$3]r^\"!#67$$\"+y/GlJF/$\"+LYnaFF^o7$$\"+urI8LF/$\"+Liy@_F^o7$$\"+D
3dlMF/$\"+]P^fxF^o7$$\"+LZo*f$F/$\"+]bu%***F^o7$$\"+F_m]PF/$\"+7(36D\"
!#57$$\"+icE-RF/$\"+.hx.:Fhp7$$\"+s2O[SF/$\"+`zEZ<Fhp7$$\"+G\"H5=%F/$
\"+!)=Qo>Fhp7$$\"+NYyQVF/$\"+DxIJAFhp7$$\"+VUUsWF/$\"+0//aCFhp7$$\"+w)
yyi%F/$\"+g988FFhp7$$\"+oD[lZF/$\"+Z4ZUHFhp7$$\"+EcX;\\F/$\"+5F4%>$Fhp
7$$\"+RhR_\\F/$\"+lN*RD$Fhp7$$\"+`mL))\\F/$\"+AW*QJ$Fhp7$$\"+!y@t*\\F/
$\"+L'p)GLFhp7$$\"+4pI1]F/$\"+LLLLLFhp7$$\"+P?H:]F/Fct7$$\"+mrFC]F/Fct
7$$\"+BuCU]F/Fct7$$\"+!o<-1&F/Fct7$$\"+!*z@N^F/Fct7$$\"+,$=-@&F/Fct7$$
\"+(plzM&F/Fct7$$\"+s[a'\\&F/Fct7$$\"+yo(3l&F/Fct7$$\"+ULA&y&F/Fct7$$
\"+tAxdeF/Fct7$$\"+07KIfF/Fct7$$\"+S(e!\\fF/Fct7$$\"+wiznfF/Fct7$$\"+7
Q`')fF/Fct7$$\"+\\8F0gF/$\"+_xaCLFhp7$$\"+@kuUgF/$\"+)H*3iKFhp7$$\"+%
\\@-3'F/$\"+V3j*>$Fhp7$$\"+$opoA'F/$\"+&><_&HFhp7$$\"+Y$f(ojF/$\"+BWt=
FFhp7$$\"+DOIElF/$\"+D1;cCFhp7$$\"+nT'ym'F/$\"+)QE-A#Fhp7$$\"+h-,>oF/$
\"+KiJo>Fhp7$$\"+(3rf&pF/$\"+)=[+u\"Fhp7$$\"+Yaq0rF/$\"+B4\\!\\\"Fhp7$
$\"+4QfYsF/$\"+&)pnb7Fhp7$$\"+VF'QR(F/$\"+i(G-,\"Fhp7$$\"+X]%y`(F/$\"+
$e#e-xF^o7$$\"+r6e)o(F/$\"+<QJ!>&F^o7$$\"+vzvLyF/$\"+</qqFF^o7$$\"+-,*
z!zF/$\"++$)\\L:F^o7$$\"+FAA#)zF/$\"+n@'H'HFY7$$\"+4WU\"*zF/$\"+n^EH9F
Y7$$\"+!fE1+)F/F+7$$\"+r(G)4!)F/F+7$$\"+^4.>!)F/F+7$$\"+8`VP!)F/F+7$$
\"+u'Re0)F/F+7$$\"+(R[E4)F/F+7$$\"+>rXH\")F/F+7$$\"+2R5(>)F/F+7$$\"+%p
]ZE)F/F+7$$\"+)R7)>%)F/F+7$$\"+N9]e&)F/F+7$$\"+vGP1()F/F+7$$\"+7Z!z%))
F/F+7$$\"\"*F*F+-%'COLOURG6&%$RGBG$\"#5!\"\"F+F+-%*AXESSTYLEG6#%$BOXG-
%%FONTG6%%&TIMESG%&ROMANG\"#;-%+AXESLABELSG6%Q!6\"Fj`lFa`l-%*AXESTICKS
G6%7&\"\"$\"\"&\"\"'\"\")7$F*$\"#L!\"#Fa`l-%%VIEWG6$;F(Fd_l%(DEFAULTG
" 1 2 0 1 10 0 2 9 1 2 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}
}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "loi de la diff\351rence  (G - F)
" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "int(f(t)*g(x+t), t=-infinity..+
infinity);\nld:= unapply(%,x):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "d
isplayg(plot(ld(x), x=0..7, axes=boxed), tickmarks=[[1,3,4,6],[0,0.33]
]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$intG6$*&,&-%*HeavisideG6#%\"
tG#\"\"\"\"\"#*&#F-F.F--F)6#,&F+F-F.!\"\"F-F4F-,&-F)6#,(%\"xGF-F+F-\"
\"$F4#F-F:*&#F-F:F--F)6#,(F9F-F+F-\"\"'F4F-F4F-/F+;,$%)infinityGF4FE" 
}}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6$7]
p7$$\"\"!F)F(7$$\"+\"z+e_\"!#5F(7$$\"+,>R`GF-F(7$$\"+`pSYVF-F(7$$\"+y'
=$\\eF-F(7$$\"+Dt3XtF-F(7$$\"+G=ZQ!)F-F(7$$\"+Lj&=t)F-F(7$$\"+zg$34*F-
F(7$$\"+Ee\")\\%*F-F(7$$\"+*p0$H'*F-F(7$$\"+tbz3)*F-F(7$$\"+40a)*)*F-F
(7$$\"+YaG))**F-F(7$$\"+QI!y+\"!\"*$\"+Lj]+8!#77$$\"+Kvx;5FU$\"+L`D'z#
FX7$$\"+0!H54\"FU$\"+$3]r^\"!#67$$\"+y/Gl6FU$\"+LYnaFF]o7$$\"+urI88FU$
\"+Liy@_F]o7$$\"+D3dl9FU$\"+]P^fxF]o7$$\"+LZo*f\"FU$\"+]bu%***F]o7$$\"
+F_m]<FU$\"+7(36D\"F-7$$\"+icE->FU$\"+.hx.:F-7$$\"+s2O[?FU$\"+`zEZ<F-7
$$\"+G\"H5=#FU$\"+!)=Qo>F-7$$\"+NYyQBFU$\"+DxIJAF-7$$\"+VUUsCFU$\"+0//
aCF-7$$\"+w)yyi#FU$\"+g988FF-7$$\"+oD[lFFU$\"+Z4ZUHF-7$$\"+EcX;HFU$\"+
5F4%>$F-7$$\"+RhR_HFU$\"+lN*RD$F-7$$\"+`mL))HFU$\"+AW*QJ$F-7$$\"+!y@t*
HFU$\"+L'p)GLF-7$$\"+4pI1IFU$\"+LLLLLF-7$$\"+P?H:IFUFat7$$\"+mrFCIFUFa
t7$$\"+BuCUIFUFat7$$\"+!o<-1$FUFat7$$\"+!*z@NJFUFat7$$\"+,$=-@$FUFat7$
$\"+(plzM$FUFat7$$\"+s[a'\\$FUFat7$$\"+yo(3l$FUFat7$$\"+ULA&y$FUFat7$$
\"+tAxdQFUFat7$$\"+07KIRFUFat7$$\"+S(e!\\RFUFat7$$\"+wiznRFUFat7$$\"+7
Q`')RFUFat7$$\"+\\8F0SFU$\"+_xaCLF-7$$\"+@kuUSFU$\"+)H*3iKF-7$$\"+%\\@
-3%FU$\"+V3j*>$F-7$$\"+$opoA%FU$\"+&><_&HF-7$$\"+Y$f(oVFU$\"+BWt=FF-7$
$\"+DOIEXFU$\"+D1;cCF-7$$\"+nT'ym%FU$\"+)QE-A#F-7$$\"+h-,>[FU$\"+KiJo>
F-7$$\"+(3rf&\\FU$\"+)=[+u\"F-7$$\"+Yaq0^FU$\"+B4\\!\\\"F-7$$\"+4QfY_F
U$\"+&)pnb7F-7$$\"+VF'QR&FU$\"+i(G-,\"F-7$$\"+X]%y`&FU$\"+$e#e-xF]o7$$
\"+r6e)o&FU$\"+<QJ!>&F]o7$$\"+vzvLeFU$\"+</qqFF]o7$$\"+-,*z!fFU$\"++$)
\\L:F]o7$$\"+FAA#)fFU$\"+n@'H'HFX7$$\"+4WU\"*fFU$\"+n^EH9FX7$$\"+!fE1+
'FUF(7$$\"+r(G)4gFUF(7$$\"+^4.>gFUF(7$$\"+8`VPgFUF(7$$\"+u'Re0'FUF(7$$
\"+(R[E4'FUF(7$$\"+>rXHhFUF(7$$\"+2R5(>'FUF(7$$\"+%p]ZE'FUF(7$$\"+)R7)
>kFUF(7$$\"+N9]elFUF(7$$\"+vGP1nFUF(7$$\"+7Z!z%oFUF(7$$\"\"(F)F(-%'COL
OURG6&%$RGBG$\"#5!\"\"F(F(-%*AXESSTYLEG6#%$BOXG-%%FONTG6%%&TIMESG%&ROM
ANG\"#;-%+AXESLABELSG6%Q!6\"Fh`lF_`l-%*AXESTICKSG6%7&\"\"\"\"\"$\"\"%
\"\"'7$F)$\"#L!\"#F_`l-%%VIEWG6$;F(Fb_l%(DEFAULTG" 1 2 0 1 10 0 2 9 1 
2 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "" 
0 "" {TEXT -1 40 "loi de la diff\351rence (dans l'autre sens)" }}
{PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "int(f(t+x)*g(t), t=-infinity..+infi
nity);\nld:= unapply(%,x):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "plot(
ld(x), x=-7..0, axes=boxed);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$int
G6$*&,&-%*HeavisideG6#,&%\"tG\"\"\"%\"xGF-#F-\"\"#*&#F-F0F--F)6#,(F,F-
F.F-F0!\"\"F-F6F-,&-F)6#,&F,F-\"\"$F6#F-F;*&#F-F;F--F)6#,&F,F-\"\"'F6F
-F6F-/F,;,$%)infinityGF6FF" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 
{PLOTDATA 2 "6&-%'CURVESG6$7]p7$$!\"(\"\"!$F*F*7$$!+@*>u%o!\"*F+7$$!+5
3m9nF/F+7$$!+0$f`c'F/F+7$$!+K\"o]T'F/F+7$$!+o7\\liF/F+7$$!+=G:'>'F/F+7
$$!+nV\"o7'F/F+7$$!+$R;44'F/F+7$$!+=%=]0'F/F+7$$!+J%pq.'F/F+7$$!+V/7>g
F/F+7$$!+]f95gF/F+7$$!+c9<,gF/F+7$$!+ip>#*fF/$\"+Lj]+8!#77$$!+oCA$)fF/
$\"+L`D'z#FY7$$!+&*4(*3fF/$\"+$3]r^\"!#67$$!+A&>Z$eF/$\"+LYnaFF^o7$$!+
EGp'o&F/$\"+Liy@_F^o7$$!+v\"HW`&F/$\"+]P^fxF^o7$$!+n_J+aF/$\"+]bu%***F
^o7$$!+tZL\\_F/$\"+7(36D\"!#57$$!+QVt(4&F/$\"+.hx.:Fhp7$$!+G#R;&\\F/$
\"+`zEZ<Fhp7$$!+s3(*=[F/$\"+!)=Qo>Fhp7$$!+l`@hYF/$\"+DxIJAFhp7$$!+dddF
XF/$\"+0//aCFhp7$$!+C67sVF/$\"+g988FFhp7$$!+Ku^MUF/$\"+Z4ZUHFhp7$$!+uV
a$3%F/$\"+5F4%>$Fhp7$$!+hQgZSF/$\"+lN*RD$Fhp7$$!+ZLm6SF/$\"+AW*QJ$Fhp7
$$!+?#yE+%F/$\"+L'p)GLFhp7$$!+\"4$p$*RF/$\"+LLLLLFhp7$$!+jzq%)RF/Fct7$
$!+MGsvRF/Fct7$$!+xDvdRF/Fct7$$!+?ByRRF/Fct7$$!+5?ykQF/Fct7$$!+*p\"y*y
$F/Fct7$$!+.V._OF/Fct7$$!+G^X.NF/Fct7$$!+AJ7\\LF/Fct7$$!+emx9KF/Fct7$$
!+FxAUJF/Fct7$$!+&zy'pIF/Fct7$$!+g7%40$F/Fct7$$!+CP?KIF/Fct7$$!+)=mM,$
F/Fct7$$!+^'GZ*HF/$\"+_xaCLFhp7$$!+zNDdHF/$\"+)H*3iKFhp7$$!+1&y(>HF/$
\"+V3j*>$Fhp7$$!+<.8tFF/$\"+&><_&HFhp7$$!+a1CJEF/$\"+BWt=FFhp7$$!+vjpt
CF/$\"+D1;cCFhp7$$!+Le8KBF/$\"+)QE-A#Fhp7$$!+R(*)4=#F/$\"+KiJo>Fhp7$$!
+8*GS/#F/$\"+)=[+u\"Fhp7$$!+aXH%*=F/$\"+B4\\!\\\"Fhp7$$!+\">1Mv\"F/$\"
+&)pnb7Fhp7$$!+ds81;F/$\"+i(G-,\"Fhp7$$!+b\\:i9F/$\"+$e#e-xF^o7$$!+H)=
9J\"F/$\"+<QJ!>&F^o7$$!+D?Cm6F/$\"+</qqFF^o7$$!+**)4?4\"F/$\"+<$)\\L:F
^o7$$!+txx<5F/$\"+n@'H'HFY7$$!+#fv&35F/$\"+L`EH9FY7$$!+:Tt$***FhpF+7$$
!+3Br,**FhpF+7$$!++0p4)*FhpF+7$$!+&)okD'*FhpF+7$$!+qKgT%*FhpF+7$$!+Sg^
t!*FhpF+7$$!*\")Gaq)F/F+7$$!+N4'*G!)FhpF+7$$!*1$\\_tF/F+7$$!*-w=!eF/F+
7$$!*l&)\\T%F/F+7$$!*Dri$HF/F+7$$!*)G&4_\"F/F+7$F+F+-%'COLOURG6&%$RGBG
$\"#5!\"\"F+F+-%*AXESSTYLEG6#%$BOXG-%+AXESLABELSG6$Q\"x6\"Q!6\"-%%VIEW
G6$;F(F+%(DEFAULTG" 1 2 0 1 10 0 2 9 1 2 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "
" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "Loi du Chi2" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "xprint(gauss);" }{TEXT -1 0 "" }}
{PARA 2 "" 1 "" {TEXT -1 267 "                                        \+
                    2\n                                               \+
  exp(- 1/2 t ) sqrt(2)\n                                        t -> \+
1/2 ---------------------\n                                           \+
            sqrt(Pi)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "# g
auss:= unapply(exp(-t^2/2)/sqrt(2*Pi),t);;" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 38 "int(gauss(t), t=-infinity..+infinity);" }{TEXT -1 
0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "" 0 
"" {TEXT -1 14 "Mauvaise fa\347on" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 
81 "Int(gauss(t), t=-infinity..+infinity); student[changevar](t^2=u, %
, u);\nvalue(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*&*&-%$
expG6#,$*$)%\"tG\"\"#\"\"\"#!\"\"F0F1-%%sqrtG6#F0F1F1*$-F56#%#PiGF1F3#
F1F0/F/;,$%)infinityGF3F?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$
,$*&*&-%$expG6#,$%\"uG#!\"\"\"\"#\"\"\"-%%sqrtG6#F0F1F1*&-F36#%#PiGF1-
F36#F-F1F/#F/\"\"%/F-;%)infinityGF?" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 6 "chi[1]" }}{PARA 0 "> " 
0 "" {MPLTEXT 1 0 96 "Int(gauss(t), t=0..+infinity); student[changevar
](t^2=u, %, u);\nchi[1]:= unapply(2*op(1,%), u);;" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%$IntG6$,$*&*&-%$expG6#,$*$)%\"tG\"\"#\"\"\"#!\"\"F0F1
-%%sqrtG6#F0F1F1*$-F56#%#PiGF1F3#F1F0/F/;\"\"!%)infinityG" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*&*&-%$expG6#,$%\"uG#!\"\"\"\"#\"\"
\"-%%sqrtG6#F0F1F1*&-F36#%#PiGF1-F36#F-F1F/#F1\"\"%/F-;\"\"!%)infinity
G" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$chiG6#\"\"\"R6#%\"uG6\"6$%)op
eratorG%&arrowGF+,$*&*&-%$expG6#,$9$#!\"\"\"\"#F'-%%sqrtG6#F9F'F'*&-F;
6#%#PiGF'-F;6#F6F'F8#F'F9F+F+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 79 "Int(chi[1](t)*chi[1](u-t), t=0..u); (xcombipo@value)(%);\nchi[
2]:= unapply(%,u);" }}{PARA 11 "" 0 "" {TEXT -1 0 "" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%$IntG6$,$*&*&-%$expG6#,$%\"tG#!\"\"\"\"#\"\"\"-F*6#
,&%\"uGF.*&#F1F0F1F-F1F1F1F1*(%#PiGF1-%%sqrtG6#F-F1-F;6#,&F5F1F-F/F1F/
F7/F-;\"\"!F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$-%$expG6#,$%\"uG#!
\"\"\"\"##\"\"\"F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$chiG6#\"\"#R
6#%\"uG6\"6$%)operatorG%&arrowGF+,$-%$expG6#,$9$#!\"\"F'#\"\"\"F'F+F+F
+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 79 "Int(chi[2](t)*chi[1](u
-t), t=0..u); (xcombipo@value)(%);\nchi[3]:= unapply(%,u);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*&*(-%$expG6#,$%\"tG#!\"\"\"\"#\"
\"\"-F*6#,&%\"uGF.*&#F1F0F1F-F1F1F1-%%sqrtG6#F0F1F1*&-F96#%#PiGF1-F96#
,&F5F1F-F/F1F/#F1\"\"%/F-;\"\"!F5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,
$*&*(-%%sqrtG6#%\"uG\"\"\"-F'6#\"\"#F*-%$expG6#,$F)#!\"\"F-F*F**$-F'6#
%#PiGF*F3#F*F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "exp(-u/2)
*u^(nu/2-1); lprint(\"--\"); int(%, u=0..infinity);\nASSERT(chi2(nu,u)
=%%/%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%$expG6#,$%\"uG#!\"\"\"
\"#\"\"\")F(\"\"%F," }}{PARA 6 "" 1 "" {TEXT -1 4 "\"--\"" }}{PARA 11 
"" 1 "" {XPPMATH 20 "6#\"$o(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 126 "ma:= Matrix([seq([seq(stats[statevalf,icdf, studentst[k]](1-j/2
), \nj=[1/3,1/20,1/100,1/1000])], \nk=[1,2,3,4,5,10,100,1000])]);" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#maG-%'RTABLEG6$\"*[NAT\"-%'MATRIXG6
#7*7&$\"+330K<!\"*$\"+u/iq7!\")$\"+;TnljF3$\"+)[#>mj!\"(7&$\"+k5\"\\E
\"F0$\"+IFl-VF0$\"+,K%[#**F0$\"+ea!*fJF37&$\"+%ev/:\"F0$\"+0jW#=$F0$\"
+5$44%eF0$\"+kyR#H\"F37&$\"+WcN*4\"F0$\"+0^WwFF0$\"+r[4/YF0$\"+\"e,.h)
F07&$\"+\"**z/2\"F0$\"+O=eqDF0$\"+%)H9KSF0$\"+Em#)ooF07&$\"+]_a;5F0$\"
+_)Q\"GAF0$\"+tEFpJF0$\"+fQ*oe%F07&$\"+FBE@(*!#5$\"+>:(R)>F0$\"+@0*ei#
F0$\"+68\\!R$F07&$\"+/+!*y'*Fco$\"+\"3RB'>F0$\"+)pa2e#F0$\"+[EG+LF0" }
}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalf(ma,3);" }}{PARA 11 "
" 1 "" {XPPMATH 20 "6#-%'RTABLEG6$\"*%y%>T\"-%'MATRIXG6#7*7&$\"$t\"!\"
#$\"$F\"!\"\"$\"$P'F1$F3\"\"!7&$\"$E\"F.$\"$I%F.$\"$#**F.$\"$;$F17&$\"
$:\"F.$\"$=$F.$\"$%eF.$\"$H\"F17&$\"$5\"F.$\"$y#F.$\"$g%F.$\"$h)F.7&$
\"$2\"F.$\"$d#F.$\"$.%F.$\"$(oF.7&$\"$-\"F.$\"$B#F.$\"$<$F.$\"$f%F.7&$
\"$s*!\"$$\"$)>F.$\"$j#F.$\"$R$F.7&$\"$o*F`o$\"$'>F.$\"$e#F.$\"$I$F." 
}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "add((k-11.75)^ 2, k=[11,1
2,14,10])/3; sqrt(%); %*3.18/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"
+nmm;H!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+G^#yq\"!\"*" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+a>W:F!\"*" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 89 "my:=99.2: add((k-my)^ 2, k=[80,115,101,97,103])/
4; sqrt(%); %*2.78/sqrt(5.);\nmy-%..my+%;\n" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#$\"++++-;!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+(Q
,dE\"!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+`!)et:!\")" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#;$\"+Z>TY$)!\")$\"+0)e$\\6!\"(" }}}}{SECT 1 
{PARA 3 "" 0 "" {TEXT -1 14 "Chi2 pour nu=1" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 45 "chi:= add((w[k]-n*p[k])^2/(n*p[k]), k=0..1);\n" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "subs([p[1]=p, p[0]=1-p], [w[
1]=w, w[0]=n-w], chi);\nnormal(%);" }}}}{SECT 1 {PARA 3 "" 0 "" {TEXT 
-1 22 "Loi de Student-Fischer" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 80 "rel:= t=u/s; nu:= 'nu':\nrel2:= t2=u2/s2;\nmap(ln,rel2); simplif
y(%,ln,symbolic);;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$relG/%\"tG*&%
\"uG\"\"\"%\"sG!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%rel2G/%#t2G
*&%#u2G\"\"\"%#s2G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#lnG6#%#
t2G-F%6#*&%#u2G\"\"\"%#s2G!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%
#lnG6#%#t2G,&-F%6#%#u2G\"\"\"-F%6#%#s2G!\"\"" }}}{EXCHG {PARA 0 "> " 
0 "" {MPLTEXT 1 0 103 "Int(gauss(u), u=0..infinity);\nstudent[changeva
r](lu2=ln(u^2),%,lu2);\nlaw_lu2:= unapply(2*op(1,%), lu2);" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*&*&-%$expG6#,$*$)%\"uG\"\"#\"\"
\"#!\"\"F0F1-%%sqrtG6#F0F1F1*$-F56#%#PiGF1F3#F1F0/F/;\"\"!%)infinityG
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*&*(-%$expG6#,$-F*6#%$l
u2G#!\"\"\"\"#\"\"\"-%%sqrtG6#F2F3-F56#F-F3F3*$-F56#%#PiGF3F1#F3\"\"%/
F/;,$%)infinityGF1FB" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%(law_lu2GR6#
%$lu2G6\"6$%)operatorG%&arrowGF(,$*&*(-%$expG6#,$-F06#9$#!\"\"\"\"#\"
\"\"-%%sqrtG6#F8F9-F;6#F3F9F9*$-F;6#%#PiGF9F7#F9F8F(F(F(" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "Int(chi2(nu,c2),c2=0..infinity);\n
student[changevar](ls2=ln(c2/nu),%,ls2);\nlaw_ls2:= unapply(op(1,%), l
s2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*&*&)%#c2G,&%#nuG#\"
\"\"\"\"#F-!\"\"F--%$expG6#,$F)#F/F.F-F-*&)F.,$F+F,F--%&GAMMAG6#F7F-F/
/F);\"\"!%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*&**)
*&-%$expG6#%$ls2G\"\"\"%#nuGF.,&F/#F.\"\"#F.!\"\"F.-F+6#,$F)#F3F2F.F*F
.F/F.F.*&)F2,$F/F1F.-%&GAMMAG6#F:F.F3/F-;,$%)infinityGF3FA" }}{PARA 
11 "" 1 "" {XPPMATH 20 "6#>%(law_ls2GR6#%$ls2G6\"6$%)operatorG%&arrowG
F(*&**)*&-%$expG6#9$\"\"\"%#nuGF4,&F5#F4\"\"#F4!\"\"F4-F16#,$F/#F9F8F4
F0F4F5F4F4*&)F8,$F5F7F4-%&GAMMAG6#F@F4F9F(F(F(" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 140 "law_ls2(x)*law_lu2(lt2+x);\nexpand(simplify(%
,exp,symbolic));\nInt(%,x=-infinity..infinity);\nstudent[changevar](x=
ln(z),%,z);\ntmp:= value(%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&
*0)*&-%$expG6#%\"xG\"\"\"%#nuGF,,&F-#F,\"\"#F,!\"\"F,-F)6#,$F'#F1F0F,F
(F,F-F,-F)6#,$-F)6#,&%$lt2GF,F+F,F5F,-%%sqrtG6#F0F,-F>6#F9F,F,*()F0,$F
-F/F,-%&GAMMAG6#FDF,-F>6#%#PiGF,F1F/" }}{PARA 11 "" 1 "" {XPPMATH 20 "
6#,$*&*0)*&-%$expG6#%\"xG\"\"\"%#nuGF,,&F-#F,\"\"#F,!\"\"F,F-F,-%%sqrt
G6#F0F,-F)6#,$F'#F1F0F,-F)6#,$F+#\"\"$F0F,-F)6#,$*&-F)6#%$lt2GF,F(F,F8
F,-F)6#,$FDF/F,F,*()F0,$F-F/F,-%&GAMMAG6#FJF,-F36#%#PiGF,F1F/" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*&*0)*&-%$expG6#%\"xG\"\"\"
%#nuGF/,&F0#F/\"\"#F/!\"\"F/F0F/-%%sqrtG6#F3F/-F,6#,$F*#F4F3F/-F,6#,$F
.#\"\"$F3F/-F,6#,$*&-F,6#%$lt2GF/F+F/F;F/-F,6#,$FGF2F/F/*()F3,$F0F2F/-
%&GAMMAG6#FMF/-F66#%#PiGF/F4F2/F.;,$%)infinityGF4FW" }}{PARA 11 "" 1 "
" {XPPMATH 20 "6#-%$IntG6$,$*&*0)*&%\"zG\"\"\"%#nuGF,,&F-#F,\"\"#F,!\"
\"F,F-F,-%%sqrtG6#F0F,-%$expG6#,$F*#F1F0F,-F36#F+F,-F66#,$*&-F66#%$lt2
GF,F+F,F9F,-F66#,$FBF/F,F,*()F0,$F-F/F,-%&GAMMAG6#FHF,-F36#%#PiGF,F1F/
/F+;\"\"!%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$tmpG*&*0)-%
$expG6#%$lt2G,&%#nuG#!\"\"\"\"##\"\"\"F0F/F2),&F2F2*&F-F2-F)6#,$F+F/F2
F2F,F2)*&%\"zGF2F-F2,&F-#F2F0F2F/F2)F;,&F-F.F2F2F2F-F2-F)6#,$F+F=F2-%&
GAMMAG6#,&F-F=F=F2F2F2*&-%%sqrtG6#%#PiGF2-FD6#,$F-F=F2F/" }}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 177 "simplify(tmp, power, symbolic);\nI
nt(%, lt2=-infinity..+infinity);\nstudent[changevar](lt2=ln(abst^2),%,
 abst);\nsimplify(%, power, symbolic): applyop(expand,1,%);\nres0:= op
(1,%);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&**-%$expG6#,$*&%$lt2G\"
\"\"%#nuGF+#!\"\"\"\"#F+),&F+F+*&F,F+-F&6#,$F*F.F+F+,&F,F-#F+F/F.F+)F,
,$F,#F+F/F+-%&GAMMAG6#,&F,F:F:F+F+F+*&-%%sqrtG6#%#PiGF+-F<6#F9F+F." }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$*&**-%$expG6#,$*&%$lt2G\"\"\"
%#nuGF.#!\"\"\"\"#F.),&F.F.*&F/F.-F)6#,$F-F1F.F.,&F/F0#F.F2F1F.)F/,$F/
#F.F2F.-%&GAMMAG6#,&F/F=F=F.F.F.*&-%%sqrtG6#%#PiGF.-F?6#F<F.F1/F-;,$%)
infinityGF1FL" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$IntG6$,$*&**-%$exp
G6#,$*&-%#lnG6#*$)%%abstG\"\"#\"\"\"F5%#nuGF5#!\"\"F4F5),&F5F5*&F6F5*$
F2F5F8F5,&F6F7#F5F4F8F5)F6,$F6#F5F4F5-%&GAMMAG6#,&F6FAFAF5F5F5*(-%%sqr
tG6#%#PiGF5-FC6#F@F5F3F5F8F4/F3;\"\"!%)infinityG" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#-%$IntG6$,$*&*(),&*$)%%abstG\"\"#\"\"\"F/%#nuGF/,$F0#!
\"\"F.F/)F0,$F0#F/F.F/-%&GAMMAG6#,&F0F6F6F/F/F/*(-%%sqrtG6#F*F/-F=6#%#
PiGF/-F86#F5F/F3F./F-;\"\"!%)infinityG" }}{PARA 11 "" 1 "" {XPPMATH 
20 "6#>%%res0G,$*&*(),&*$)%%abstG\"\"#\"\"\"F.%#nuGF.,$F/#!\"\"F-F.)F/
,$F/#F.F-F.-%&GAMMAG6#,&F/F5F5F.F.F.*(-%%sqrtG6#F)F.-F<6#%#PiGF.-F76#F
4F.F2F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "res:= xcombipo(s
ubs(abst=t,res0))/2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$resG*&*(),&
*$)%\"tG\"\"#\"\"\"F-%#nuGF-,&F.#!\"\"F,#F-F,F1F-)F.,$F.#F-F,F--%&GAMM
AG6#,&F.F5F5F-F-F-*&-F76#F4F--%%sqrtG6#%#PiGF-F1" }}}{EXCHG {PARA 0 ">
 " 0 "" {MPLTEXT 1 0 73 "res_th:= GAMMA( (nu+1)/2 )/GAMMA(nu/2)/sqrt(n
u*Pi)/(1+t^2/nu)^((nu+1)/2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'res
_thG*&-%&GAMMAG6#,&%#nuG#\"\"\"\"\"#F+F,F,*(-F'6#,$F*F+F,-%%sqrtG6#*&F
*F,%#PiGF,F,),&F,F,*&*$)%\"tGF-F,F,F*!\"\"F,F)F,F=" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 51 "xcombipo(res/res_th);\nsimplify(%, power, s
ymbolic);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**-%%sqrtG6#%#nuG\"\"\"),
&*$)%\"tG\"\"#F(F(F'F(,&F'#!\"\"F.#F(F.F1F()F',$F'#F(F.F()*&F*F(F'F1,&
F'F5F5F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "7 0 0" 39 }{VIEWOPTS 1 
1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }{RTABLE_HANDLES 
141223548 141194784 }{RTABLE 
M6R0
I6RTABLE_SAVE/141223548X,%)anythingG6"6"][[[[[pA")"%$"+330K<!"*$"+k5"\E"F)$"+%e
v/:"F)$"+WcN*4"F)$"+"**z/2"F)$"+]_a;5F)$"+FBE@(*!#5$"+/+!*y'*F6$"+u/iq7!")$"+IF
l-VF)$"+0jW#=$F)$"+0^WwFF)$"+O=eqDF)$"+_)Q"GAF)$"+>:(R)>F)$"+"3RB'>F)$"+;TnljF;
$"+,K%[#**F)$"+5$44%eF)$"+r[4/YF)$"+%)H9KSF)$"+tEFpJF)$"+@0*ei#F)$"+)pa2e#F)$"+
)[#>mj!"($"+ea!*fJF;$"+kyR#H"F;$"+"e,.h)F)$"+Em#)ooF)$"+fQ*oe%F)$"+68\!R$F)$"+[
EG+LF)F&
}
{RTABLE 
M6R0
I6RTABLE_SAVE/141194784X,%)anythingG6"6"][[[[[pA")"%$"$t"!"#$"$E"F)$"$:"F)$"$5"
F)$"$2"F)$"$-"F)$"$s*!"$$"$o*F6$"$F"!""$"$I%F)$"$=$F)$"$y#F)$"$d#F)$"$B#F)$"$)>
F)$"$'>F)$"$P'F;$"$#**F)$"$%eF)$"$g%F)$"$.%F)$"$<$F)$"$j#F)$"$e#F)$FK""!$"$;$F;
$"$H"F;$"$h)F)$"$(oF)$"$f%F)$"$R$F)$"$I$F)F&
}