{VERSION 5 0 "IBM INTEL NT" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 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 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 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 "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Times" 1 12 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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "m:=1005010010005001: ifactor(m);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#*()-%!G6#\"\"(\"\"&\"\"\")-F&6#\"#6F)F*)-F&6#\"# 8F)F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "a:=888888888888888 :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "a mod 7; a mod 11; a m od 13;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"%" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "a7:=a mod 7^5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "aux:=a7^2 mod 7^5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "aux:=aux^1 mod 7^5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "for i to 3 do aux:=aux^7 mod 7^5 en d do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "aux;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "a11:=a mod 11^5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "a ux:=a11^2 mod 11^5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "aux: =aux^5 mod 11^5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "for i t o 3 do aux:=aux^11 mod 11^5 end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "aux;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "a13:=a mod 13^5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "aux:=a13^2 mod 13^5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "aux:=aux^3 mod 13^5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "for i to 3 do aux:=aux^13 mod 13^5 \+ end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 4 "aux;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "lcm(2*7^3,2*5*11^3,2*3*13^3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #\",I+4!4I" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "ifactor(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*.-%!G6#\"\"#\"\"\"-F%6#\"\"$F(-F%6# \"\"&F()-F%6#\"\"(F+F()-F%6#\"#6F+F()-F%6#\"#8F+F(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q4" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 66 "restart: with(stats): n:=100: dot:=proc(a);add(a[j ]^2,j=1..6)end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "dis:=pro c(a);sqrt(add((a[j]-a[j+3])^2,j=1..3))end:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 38 "X:=[seq([random[normald](6)],i=1..n)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "f:=exp(-sqrt(x[1]^2+x[2]^2+x[3]^2) -sqrt(x[4]^2+x[5]^2+x[6]^2))/\n(1+sqrt(x[1]^2+x[2]^2+x[3]^2)+sqrt(x[4] ^2+x[5]^2+x[6]^2)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "F:=[ seq(simplify(diff(f,x[i])/f/2),i=1..6)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "At:=[]: Bt:=[]: tau:=.5:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 340 "for k to 100 do A:=0: B:=0:\nfor i to n do Fo:=tau *eval(F,x=X[i]):\nxn:=X[i]+[sqrt(tau)*random[normald](6)]+Fo: Fn:=t au*eval(F,x=xn):\nT:=eval(f,x=xn)/eval(f,x=X[i])*exp((dot(xn-X[i]-Fo)- dot(X[i]-xn-Fn))/tau/2):\nif random[uniform]() " 0 "" {MPLTEXT 1 0 12 "with(pl ots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "pointplot([seq([i, At[i]],i=1..100)]); add(At[i],i=1..100)/100;" }}{PARA 13 "" 1 "" {GLPLOT2D 768 317 317 {PLOTDATA 2 "6#-%'POINTSG6`q7$$\"\"\"\"\"!$\"+2; ,/S!\"*7$$\"\"#F)$\"+^Uc#f$F,7$$\"#:F)$\"+)>*[xNF,7$$\"#;F)$\"+?&=%oPF,7$$\"#F)$\"+UR^3PF,7$$\"#?F)$\"+@k-yOF,7$$\"# @F)$\"+>-ohPF,7$$\"#AF)$\"+m%Gu\"QF,7$$\"#BF)$\"+Lwv,PF,7$$\"#CF)$\"+q +tqRF,7$$\"#DF)$\"+3NvgSF,7$$\"#EF)$\"+Ak$R6%F,7$$\"#FF)$\"+ApVHSF,7$$ \"#GF)$\"+)*)30&RF,7$$\"#HF)$\"+1zRePF,7$$\"#IF)$\"+mT5'yJPF,7$$\"#\\F)$\"+Ab'*zRF,7$$\"#]F)$\"+U-]oRF,7$$\"#^F)$\"+vO B**QF,7$$\"#_F)$\"+a\"\\g5%F,7$$\"#`F)$\"+gZ+4SF,7$$\"#aF)$\"+Ee@:SF,7 $$\"#bF)$\"+3z(p(RF,7$$\"#cF)$\"+ze,8RF,7$$\"#dF)$\"+:!*HySF,7$$\"#eF) $\"+A'\\h,%F,7$$\"#fF)$\"+F4OnSF,7$$\"#gF)$\"+(p4-+%F,7$$\"#hF)$\"+'=B <$RF,7$$\"#iF)$\"+X:$>5%F,7$$\"#jF)$\"+IjVASF,7$$\"#kF)$\"+jW!45%F,7$$ \"#lF)$\"+<_'*=TF,7$$\"#mF)$\"+w%G*)*RF,7$$\"#nF)$\"+0`O?PF,7$$\"#oF)$ \"+L&3Lf$F,7$$\"#pF)$\"+A!>4s$F,7$$\"#qF)$\"+36m " 0 "" {MPLTEXT 1 0 62 "pointplot([seq([i,Bt[i]],i=1..100)] ); add(Bt[i],i=1..100)/100;" }}{PARA 13 "" 1 "" {GLPLOT2D 872 330 330 {PLOTDATA 2 "6#-%'POINTSG6`q7$$\"\"\"\"\"!$\"+6UGwM!#57$$\"\"#F)$\"+k( 3:!QF,7$$\"\"$F)$\"+@\"*zKOF,7$$\"\"%F)$\"+kh;hIF,7$$\"\"&F)$\"+u*fGA$ F,7$$\"\"'F)$\"+?h'[U$F,7$$\"\"(F)$\"+$ppOk$F,7$$\"\")F)$\"+d!f!ROF,7$ $\"\"*F)$\"+kHNFOF,7$$\"#5F)$\"+A&=Tm$F,7$$\"#6F)$\"+ERl5OF,7$$\"#7F)$ \"+4+e4QF,7$$\"#8F)$\"+!=mf%QF,7$$\"#9F)$\"+0gnYVF,7$$\"#:F)$\"+6Q!o'R F,7$$\"#;F)$\"+zP!*HOF,7$$\"# F)$\"+%eTIb$F,7$$\"#?F)$\"+*>iLl$F,7$$\"#@F)$\"+uJYlSF,7$$\"#AF)$\"+a# [2#RF,7$$\"#BF)$\"+8\"\\SG%F,7$$\"#CF)$\"+i%\\eS$F,7$$\"#DF)$\"+wN+HLF ,7$$\"#EF)$\"+$**[0C$F,7$$\"#FF)$\"+)>b5!QF,7$$\"#GF)$\"+*3&*Ri$F,7$$ \"#HF)$\"+e.)=\"RF,7$$\"#IF)$\"+0)[d$QF,7$$\"#JF)$\"+_Zs7QF,7$$\"#KF)$ \"+6?V>UF,7$$\"#LF)$\"+dBU@SF,7$$\"#MF)$\"+QrC@QF,7$$\"#NF)$\"+\"yor/% F,7$$\"#OF)$\"+sx'[:%F,7$$\"#PF)$\"+q.\\yVF,7$$\"#QF)$\"+lVwkRF,7$$\"# RF)$\"+lo/XSF,7$$\"#SF)$\"+@/VEQF,7$$\"#TF)$\"+4r[.OF,7$$\"#UF)$\"+^7d XQF,7$$\"#VF)$\"+4GK1TF,7$$\"#WF)$\"+#R\\xn$F,7$$\"#XF)$\"+L`%3q$F,7$$ \"#YF)$\"+gIaJMF,7$$\"#ZF)$\"+g]o+OF,7$$\"#[F)$\"+t2t!f$F,7$$\"#\\F)$ \"+)p_\">LF,7$$\"#]F)$\"+\"))4!zKF,7$$\"#^F)$\"+l\"fKn$F,7$$\"#_F)$\"+ pw*3L$F,7$$\"#`F)$\"+XCk#\\$F,7$$\"#aF)$\"+_(>#*H$F,7$$\"#bF)$\"+zXhOM F,7$$\"#cF)$\"+1*)e'[$F,7$$\"#dF)$\"+wK_\"R$F,7$$\"#eF)$\"+79\"HE$F,7$ $\"#fF)$\"+d(Rr_$F,7$$\"#gF)$\"+3u5\\NF,7$$\"#hF)$\"+0quHOF,7$$\"#iF)$ \"+N%4,A$F,7$$\"#jF)$\"+NI@5LF,7$$\"#kF)$\"+Hlb@LF,7$$\"#lF)$\"+6Z\"y& QF,7$$\"#mF)$\"+L0]ANF,7$$\"#nF)$\"+)*\\H7QF,7$$\"#oF)$\"+!zCu'QF,7$$ \"#pF)$\"+;%)y)p$F,7$$\"#qF)$\"+'R#oaOF,7$$\"#rF)$\"+T<)Hi$F,7$$\"#sF) $\"+3lMCRF,7$$\"#tF)$\"+'*[S\\MF,7$$\"#uF)$\"+bf,fSF,7$$\"#vF)$\"+!*Hd pRF,7$$\"#wF)$\"+VZCHRF,7$$\"#xF)$\"+$4_*yQF,7$$\"#yF)$\"+DbqYPF,7$$\" #zF)$\"+e(*zYQF,7$$\"#!)F)$\"+A%*=QXF,7$$\"#\")F)$\"+)R/*[QF,7$$\"##)F )$\"+GqzoOF,7$$\"#$)F)$\"+'=EV)QF,7$$\"#%)F)$\"+khC]PF,7$$\"#&)F)$\"+C x,2RF,7$$\"#')F)$\"+![lii$F,7$$\"#()F)$\"+nC?sQF,7$$\"#))F)$\"+UZw-PF, 7$$\"#*)F)$\"+\\(Q\\#RF,7$$\"#!*F)$\"+y%y?e$F,7$$\"#\"*F)$\"+[;D*o$F,7 $$\"##*F)$\"+M'Gbb$F,7$$\"#$*F)$\"+B*\\tD$F,7$$\"#%*F)$\"+?G`$e$F,7$$ \"#&*F)$\"+,$*f1MF,7$$\"#'*F)$\"+R0![&RF,7$$\"#(*F)$\"+7jmdSF,7$$\"#)* F)$\"+\\f%)**QF,7$$\"#**F)$\"+W2\")QRF,7$$\"$+\"F)$\"+_'ysH$F," 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+M#y^q$!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q2" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "restart: \+ f:=2*x/b^2*exp(-x^2/b^2): assume((t*b^2-1)/b^2<0): int(exp(t*x^2)*f ,x=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&\"\"\"F%,&*&%# t|irGF%)%#b|irG\"\"#F%F%F%!\"\"F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "M:=1/(1-b^2*t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "mtaylor(ln(M),t,5);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#,**&%#t|irG\"\"\")%#b|irG\"\"#F&F&*&#F&F)F&*&)F%F)F&)F(\"\"%F&F&F&*& #F&\"\"$F&*&)F%F2F&)F(\"\"'F&F&F&*&#F&F/F&*&)F%F/F&)F(\"\")F&F&F&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "mu:=b^2: var:=b^4: k3:=2*b ^6: k4:=6*b^8: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "g0:=b : g1:=1/2/g0: g2:=-1/4/g0^3: g3:=3/8/g0^5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "EV:=g0+g2*var/2/n;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#EVG,&%#b|irG\"\"\"*(\"\")!\"\"F&F'%\"nGF*F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "V:=g1^2*var/n+(g1*g2*k3+g2^2*var^2/2+g1*g 3*var^2)/n^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG,&*(\"\"%!\"\"% #b|irG\"\"#%\"nGF(\"\"\"*(\"#KF(F)F*F+!\"#F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "Cum3:=simplify(g1^3*k3+3*g1^2*g2*var^2)/n^2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%Cum3G,$*(\"#;!\"\"%#b|irG\"\"$%\"nG !\"#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "Cum4:=g1^2*(g 1^2*k4+12*g1*g2*k3*var+12*g2^2*var^3+4*g1*g3*var^3)/n^3;" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%%Cum4G\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 110 "pdf:=(exp(-z^2/2)/sqrt(2*Pi)*(1+Cum3/6/b^3*8*n^(3/2) *z*(z^2-3)+Cum3^2/72/b^6*(4*n)^3*(z^6-15*z^4+45*z^2-15)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$pdfG,$*&#\"\"\"\"\"#F(**-%$expG6#,$*&F)! \"\"%\"zGF)F0F(F)F'%#PiG#F0F),(F(F(**\"#7F0%\"nGF3F1F(,&*$)F1F)F(F(\" \"$F0F(F(*(\"$)GF0F7F0,**$)F1\"\"'F(F(*&\"#:F()F1\"\"%F(F0*&\"#XF(F:F( F(FCF0F(F(F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "res:=ev al(pdf,z=(B-beta(1-1/4/n))/beta/(1-1/16/n)*2*sqrt(n))/beta/(1-1/16/n)* 2*sqrt(n);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%$resG*0-%$expG6#,$*,\" \"#\"\"\",&%\"BGF,-%%betaG6#,&F,F,*&F,F,*&\"\"%F,%\"nGF,!\"\"F7F7F+F0! \"#,&F,F,*&F,F,*&\"#;F,F6F,F7F7F8F6F,F7F,F+#F,F+%#PiG#F7F+,(F,F,*&#F, \"\"'F,**F-F,F0F7F9F7,&*,F5F,F-F+F0F8F9F8F6F,F,\"\"$F7F,F,F,*&#F,\"$)G F,*&F6F7,**,\"#kF,F-FCF0!\"'F9FOF6FGF,*,\"$S#F,F-F5F0!\"%F9FRF6F+F7*, \"$!=F,F-F+F0F8F9F8F6F,F,\"#:F7F,F,F,F,F0F7F9F7F6F=" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "res:=eval(res,\{n=15,beta=2\}):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "plot(res,B=1..3.2);" }} {PARA 13 "" 1 "" {GLPLOT2D 666 247 247 {PLOTDATA 2 "6%-%'CURVESG6$7`o7 $$\"\"\"\"\"!$\"3eX\"Gj=Ro<\"!#@7$$\"3omm;RP&z/\"!#<$\"3e%*eedSWhPF-7$ $\"3SL$37.y'*3\"F1$\"3Qgkv*f!)*e\"*F-7$$\"3dmmTh8gO6F1$\"3!fh!\\=3YXA! #?7$$\"3imm\"*Hd$Q=\"F1$\"3-\"Qzj=!Qe]F>7$$\"3NL$37$$\"3um;aq(HWF\"F1$\"3KmO9aXd`>FI7$$\"32+](Gle&>8F1$\"3)*4Af^# f<^$FI7$$\"3#omTv+JiO\"F1$\"3]_H1[Q5.hFI7$$\"32+]P$o`FT\"F1$\"361Bc@GG 15!#=7$$\"3_LL$Q(zgg9F1$\"3Fe_uO$H5g\"Fhn7$$\"3pmm\"*e!eF]\"F1$\"3c+2T /Zc:BFhn7$$\"35++]r!4-b\"F1$\"3I;5&*)>V.O$Fhn7$$\"3/++]A\\&yf\"F1$\"3u :tfS7#Gn%Fhn7$$\"3;++]G0xV;F1$\"3uwp=!3Wd;'Fhn7$$\"3YL3-8%=Ym\"F1$\"3< aa@s#=S!pFhn7$$\"3wm;a(Hmao\"F1$\"3qV*=m#yLqwFhn7$$\"3/+vo[kD5w/xF6\"F17$$\"3!o;/Y?w9!=F1$ \"3czxA,\"H%*>\"F17$$\"30+]()*y/f#=F1$\"3%4Uvj'*R,G\"F17$$\"3kmT5F#Gv% =F1$\"3ueb\"RX!3X8F17$$\"3CLLLk;:p=F1$\"3u+7$f\"Hm-9F17$$\"3++]()R.g;> F1$\"3MvE\"RzQ#)\\\"F17$$\"3/++v>:>R>F1$\"3irr]y,+F:F17$$\"31+]i*p#yh> F1$\"31F1$\"3uMFJ%=#oY:F17$$\"3K$eRFYoN(> F1$\"3q&oal!3S[:F17$$\"3;voHW8Yz>F1$\"37Qc-#f4$\\:F17$$\"3wmT&eAa`)>F1 $\"3kc))yx'4%\\:F17$$\"3Qe9T2rC\"*>F1$\"39ojK]Mq[:F17$$\"3A](o*))*Rr*> F1$\"3%>&)pA`%>Z:F17$$\"3iTg_qG..?F1$\"3]^.2mx)[a\"F17$$\"3YLL3_d#*3?F 1$\"3Z%*Hp%>*yT:F17$$\"3cLeRrIFhn7$$\"3*)****\\#3YX^#F1$\"3ik!*HiV9!=#F hn7$$\"3cm;a84fdDF1$\"3%f#e--0Y%e\"Fhn7$$\"3F++]$G]Yg#F1$\"3=K:`%[y&*3 \"Fhn7$$\"3AL$3K[H*[EF1$\"3;G*R%yhhzuFI7$$\"3)***\\P0S@&p#F1$\"3'*fpJG 0?F\\FI7$$\"3LLL$eel/u#F1$\"34KcO#QH0?$FI7$$\"3s**\\(ozRyy#F1$\"3'Q9(* GnP&))>FI7$$\"3,nmm#zmM$GF1$\"3&)>Tro@wG7FI7$$\"3;nm\"f)p7!)GF1$\"3A_* \\)oCyQtF>7$$\"3ML$3#43SEHF1$\"3oI'o$*3o9I%F>7$$\"3;+++Z;#*oHF1$\"3?Li 4TmizDF>7$$\"3gLLeD`l7$$\"31nmm3LChIF1$\"3V/r^Drt JzF-7$$\"3B+]()*=_JF1$\"3[P,'=RY5 D#F-7$$\"3;+++++++KF1$\"33\\7;1nB96F--%'COLOURG6&%$RGBG$\"#5!\"\"$F*F* Fbal-%+AXESLABELSG6$Q\"B6\"Q!Fgal-%%VIEWG6$;F($\"#KFaal%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "int(f,x=0..u); with(stats): \+ Ba:=[]: n:=1000:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%$expG6#,$*&% \"uG\"\"#%#b|irG!\"#!\"\"F-\"\"\"F." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "for i to n do U:=random[uniform](15): X:=[seq(2*sqrt (-ln(1-U[i])),i=1..15)]: Ba:=[op(Ba),sqrt(add(X[i]^2,i=1..15)/15)] end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "psi:=u->max(1-u^2,0 )*3/4: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "m:=add(Ba[i],i= 1..n)/n: sd:=sqrt(add((Ba[i]-m)^2,i=1..n)/n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "h:=2*sd/n^0.2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "g:=add(psi((B-Ba[i])/h),i=1..n)/n/h:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "plot(\{g,res\},B=1..3.2);" }}{PARA 13 "" 1 "" {GLPLOT2D 742 264 264 {PLOTDATA 2 "6&-%'CURVESG6$7`o7$$\"\" \"\"\"!$\"3eX\"Gj=Ro<\"!#@7$$\"3omm;RP&z/\"!#<$\"3e%*eedSWhPF-7$$\"3SL $37.y'*3\"F1$\"3Qgkv*f!)*e\"*F-7$$\"3dmmTh8gO6F1$\"3!fh!\\=3YXA!#?7$$ \"3imm\"*Hd$Q=\"F1$\"3-\"Qzj=!Qe]F>7$$\"3NL$37$$\"3um;aq(HWF\"F1$\"3KmO9aXd`>FI7$$\"32+](Gle&>8F1$\"3)*4Af^#f<^$F I7$$\"3#omTv+JiO\"F1$\"3]_H1[Q5.hFI7$$\"32+]P$o`FT\"F1$\"361Bc@GG15!#= 7$$\"3_LL$Q(zgg9F1$\"3Fe_uO$H5g\"Fhn7$$\"3pmm\"*e!eF]\"F1$\"3c+2T/Zc:B Fhn7$$\"35++]r!4-b\"F1$\"3I;5&*)>V.O$Fhn7$$\"3/++]A\\&yf\"F1$\"3u:tfS7 #Gn%Fhn7$$\"3;++]G0xV;F1$\"3uwp=!3Wd;'Fhn7$$\"3YL3-8%=Ym\"F1$\"3w/xF6\"F17$$\"3!o;/Y?w9!=F1$\"3czxA ,\"H%*>\"F17$$\"30+]()*y/f#=F1$\"3%4Uvj'*R,G\"F17$$\"3kmT5F#Gv%=F1$\"3 ueb\"RX!3X8F17$$\"3CLLLk;:p=F1$\"3u+7$f\"Hm-9F17$$\"3++]()R.g;>F1$\"3M vE\"RzQ#)\\\"F17$$\"3/++v>:>R>F1$\"3irr]y,+F:F17$$\"31+]i*p#yh>F1$\"31 F1$\"3uMFJ%=#oY:F17$$\"3K$eRFYoN(>F1$\"3q &oal!3S[:F17$$\"3;voHW8Yz>F1$\"37Qc-#f4$\\:F17$$\"3wmT&eAa`)>F1$\"3kc) )yx'4%\\:F17$$\"3Qe9T2rC\"*>F1$\"39ojK]Mq[:F17$$\"3A](o*))*Rr*>F1$\"3% >&)pA`%>Z:F17$$\"3iTg_qG..?F1$\"3]^.2mx)[a\"F17$$\"3YLL3_d#*3?F1$\"3Z% *Hp%>*yT:F17$$\"3cLeRrIFhn7$$\"3*)****\\#3YX^#F1$\"3ik!*HiV9!=#Fhn7$$ \"3cm;a84fdDF1$\"3%f#e--0Y%e\"Fhn7$$\"3F++]$G]Yg#F1$\"3=K:`%[y&*3\"Fhn 7$$\"3AL$3K[H*[EF1$\"3;G*R%yhhzuFI7$$\"3)***\\P0S@&p#F1$\"3'*fpJG0?F\\ FI7$$\"3LLL$eel/u#F1$\"34KcO#QH0?$FI7$$\"3s**\\(ozRyy#F1$\"3'Q9(*GnP&) )>FI7$$\"3,nmm#zmM$GF1$\"3&)>Tro@wG7FI7$$\"3;nm\"f)p7!)GF1$\"3A_*\\)oC yQtF>7$$\"3ML$3#43SEHF1$\"3oI'o$*3o9I%F>7$$\"3;+++Z;#*oHF1$\"3?Li4Tmiz DF>7$$\"3gLLeD`l7$$\"31nmm3LChIF1$\"3V/r^DrtJzF-7 $$\"3B+]()*=_JF1$\"3[P,'=RY5D#F-7 $$\"3;+++++++KF1$\"33\\7;1nB96F--%'COLOURG6&%$RGBG$\"#5!\"\"$F*F*Fbal- F$6$7`o7$F($\"3G)Q\\Tuk8m&F>7$F/$\"3?A%fHKl_G(F>7$F5$\"3zu8j6Gs1'*F>7$ F:$\"3#)\\n'R\\?Q7\"FI7$F@$\"3co$3.nQ&G9FI7$FE$\"3?e&RQ%RR<;FI7$FK$\"3 #4Uep!zUn:FI7$$\"3GL$3<@%*pH\"F1$\"3DPpld0G3=FI7$FP$\"3A]2mI3V!G#FI7$$ \"3WL$3-$[*GM\"F1$\"3;_pV_2m[LFI7$FU$\"32Z:D=KLKZFI7$$\"3WL$eaM#\\*Q\" F1$\"3S#esB[g^l'FI7$FZ$\"3K\">XPXKs\\*FI7$Fjn$\"3%fQ+.S\"HB;Fhn7$F_o$ \"30jo7B]?8BFhn7$Fdo$\"31EVm*eO(HLFhn7$$\"33+++(*>.u:F1$\"3_Y!phy^](RF hn7$Fio$\"3KaE*[kxvu%Fhn7$$\"3+++]DF\"3i\"F1$\"3!R%3H+?JdcFhn7$F^p$\"3 uLF.@-%Rx'Fhn7$Fcp$\"3P0$*R=dkOxFhn7$Fhp$\"3#)*>CHD=Rp)Fhn7$F]q$\"3g\" *oJ^>6k'*Fhn7$Fbq$\"3'epgZ%pUZ5F17$Fgq$\"3eo*G2MR+4\"F17$F\\r$\"3?4e#e je88\"F17$Ffr$\"3_ee*y=X=C\"F17$F`s$\"3dU,%z!4m=8F17$Fes$\"3P(pCP\"*=I W\"F17$Fjs$\"3oU#[+B-/[\"F17$F_t$\"3F)*49>X=.:F17$Fdt$\"3D!)[%GzmY]\"F 17$Fit$\"3NU%H'yPc-:F17$F^u$\"3GGn*)fy4+:F17$Fcu$\"3%f:%3e6g&\\\"F17$F ]v$\"3o(>0WA/'z9F17$Fgv$\"3m.9`]bpi9F17$Faw$\"3y&yBgycSQ\"F17$Ffw$\"3& ox)[$y^)>8F17$F[x$\"3$=\\HbAj&Q7F17$Fex$\"3w'o>PV-1=\"F17$F_y$\"3u+/M \"QEz1\"F17$Fdy$\"3;`I'QdLY)**Fhn7$Fiy$\"3>#H@5`k\">#*Fhn7$F^z$\"3sAsg r?&4K)Fhn7$Fcz$\"3[NaS-9%[X(Fhn7$Fhz$\"3]BA*f?a&[)FI7$F[]l$\"3V+xE _IU4gFI7$F`]l$\"32C\"f(G%>#3WFI7$Fe]l$\"3U6DP>bb*>$FI7$Fj]l$\"3]KDV\\_ d%Q#FI7$F_^l$\"3]LXb;6Ip;FI7$Fd^l$\"3I;T9Qq)))G'F>7$Fi^l$\"3-wU9)o^Gb# F>7$F^_lFbal7$Fc_lFbal7$Fh_lFbal7$F]`lFbal7$Fb`lFbal7$Fg`lFbal-F\\al6& F^alFbalF_alFbal-%+AXESLABELSG6$Q\"B6\"Q!Fj^m-%%VIEWG6$;F($\"#KFaal%(D EFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curv e 1" "Curve 2" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q1" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "f:=2*x*(x-y): mx:=int(int(x* f,y=-x..x),x=0..1): my:=int(int(y*f,y=-x..x),x=0..1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "m20:=int(int((x-mx)^2*f,y=-x..x),x= 0..1): m02:=int(int((y-my)^2*f,y=-x..x),x=0..1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "m11:=int(int((x-mx)*(y-my)*f,y=-x..x),x=0..1) : m22:=int(int((x-mx)^2*(y-my)^2*f,y=-x..x),x=0..1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "m22/n^3+(n-1)*(m02*m20+2*m11^2)/n^3;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(\"$>(\"\"\"\"']iB!\"\"%\"nG!\"$F&* *\"$7#F&\"&D1&F(,&F)F&F&F(F&F)F*F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*( \"'](3(!\"\",&\"$6)F&*&\"%oH\"\"\"%\"nGF+F+F+F,!\"$F+" }}}}{MARK "53 0 1" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }