{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 "Warning" -1 7 1 {CSTYLE "" -1 -1 "Courier" 1 10 0 0 255 1 2 2 2 2 2 1 1 1 3 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 P lot" -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 "Q1" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart: with(linalg):" }} {PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and tra ce have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 91 "V:=evalm(1.*matrix(5,5,[11,-4,3,-2,7,-4,5,-2,1,-6,3,- 2,9,0,10,-2,1,0,1,-2,7,-6,10,-2,17]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG-%'matrixG6#7'7'$\"#6\"\"!$!\"%F,$\"\"$F,$!\"#F,$\"\"(F,7' F-$\"\"&F,F1$\"\"\"F,$!\"'F,7'F/F1$\"\"*F,$F,F,$\"#5F,7'F1F8F?F8F17'F3 F:F@F1$\"# " 0 "" {MPLTEXT 1 0 84 "det(submat rix(V,1..1,1..1));det(submatrix(V,1..2,1..2));det(submatrix(V,1..3,1.. 3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#6\"\"!" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"#R\"\"!" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$5$ \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "det(submatrix(V,1. .4,1..4)); det(V);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$w\"\"\"!" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"$W\"\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A:=matrix(5,5,0):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "for i to 5 do A[i,i]:=sqrt(evalm(V-transpose(A)&*A)[ i,i]); for j from i+1 to 5 do A[i,j]:=x;\nA[i,j]:=solve(evalm(V-transp ose(A)&*A)[i,j],x) end do end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "evalm(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrix G6#7'7'$\"+!zCmJ$!\"*$!+y`/17F*$\"+Q.MX!*!#5$!+#*oAIgF/$\"+7%z06#F*7' \"\"!$\"+Wx$H)=F*$!+%\\X!G[F/$\"+\\OT[9F/$!+)GdY$=F*7'F5F5$\"+yqM>GF*$ \"+>.s#=#F/$\"+2l[`(F/$!+'z]GN\"F*7'F5F5F5F5$\"+Z. MX!*F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "mu:=[3,-4,2,0,5]: sigma:=vector(5): x:=[1.5,0,-1.2,0,7]:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 44 "for i to 5 do sigma[i]:=sqrt(V[i,i]) end do:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 96 "rho:=matrix(5,5): for i to \+ 5 do for j to 5 do rho[i,j]:=V[i,j]/sigma[i]/sigma[j] end do end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 224 "pc:=proc(i,j) local n; \+ n:=nops(j); if(n>0) then (pc(i,j[1..n-1])-pc([i[1],j[n]],j[1..n-1])*pc ([i[2],j[n]],j[1..n-1]))/sqrt(1-pc([i[1],j[n]],j[1..n-1])^2)/sqrt(1-pc ([i[2],j[n]],j[1..n-1])^2) else rho[op(sort(i))] end if end:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 122 "cs:=proc(i,j) local n; n:=n ops(j); if(n>0) then cs(i,j[1..n-1])*sqrt(1-pc([i,j[n]],j[1..n-1])^2) \+ else sigma[i] end if end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 173 "cm:=proc(i,j) local n; n:=nops(j); if(n>0) then cm(i,j[1..n-1])+c s(i,j[1..n-1])*pc([i,j[n]],j[1..n-1])*(x[j[n]]-cm(j[n],j[1..n-1]))/cs( j[n],j[1..n-1]) else mu[i] end if end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "pc([2,4],[1,3,5]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #$!+x2p#Q&!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "cm(2,[1,3, 5]); cm(4,[1,3,5]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+3i%zN'!\"* " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$!+nC61:!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "cs(2,[1,3,5]); cs(4,[1,3,5]);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"+!\\/oT\"!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+zOMp\\!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q2" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "restart : with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have been redefined and unprotected\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "rho[1]:=solve(rho[1]=alpha[1 ]+alpha[2]*rho[1],rho[1]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "rho[0]:=1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "for k fro m 2 to 15 do \nrho[k]:=alpha[1]*rho[k-1]+alpha[2]*rho[k-2] end do:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 187 "for i from 4 to 6 do V:=m atrix(i,i);\nfor j to i do for k to i do V[j,k]:=rho[abs(j-k)]*sigma^2 /(1-rho[1]*alpha[1]-rho[2]*alpha[2])\nend do end do;\nprint(inverse(V) ); print(det(V)) end do:" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG 6#7&7&*&\"\"\"F)*$)%&sigmaG\"\"#F)!\"\",$*&F,!\"#&%&alphaG6#F)F)F.,$*& &F36#F-F)F,F1F.\"\"!7&F/*&F,F1,&F)F)*$)F2F-F)F)F)*(F2F)F,F1,&F)F.F7F)F )F57&F5F?F;F/7&F9F5F/F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(%&sigma G\"\"),&\"\"\"F(&%&alphaG6#\"\"#F(!\"\",.F(F-F)F(*$)&F*6#F(F,F(F(*&F)F (F0F(F(*$)F)F,F(F(*$)F)\"\"$F(F-F-F-" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#-%'matrixG6#7'7'*&\"\"\"F)*$)%&sigmaG\"\"#F)!\"\",$*&F,!\"#&%&alphaG 6#F)F)F.,$*&&F36#F-F)F,F1F.\"\"!F97'F/*&F,F1,&F)F)*$)F2F-F)F)F)*(F2F)F ,F1,&F)F.F7F)F)F5F97'F5F?*&F,F1,(F=F)*$)F7F-F)F)F)F)F)F?F57'F9F5F?F;F/ 7'F9F9F5F/F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(%&sigmaG\"#5,&\"\" \"F(&%&alphaG6#\"\"#F(!\"\",.F(F-F)F(*$)&F*6#F(F,F(F(*&F)F(F0F(F(*$)F) F,F(F(*$)F)\"\"$F(F-F-F-" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG 6#7(7(*&\"\"\"F)*$)%&sigmaG\"\"#F)!\"\",$*&F,!\"#&%&alphaG6#F)F)F.,$*& &F36#F-F)F,F1F.\"\"!F9F97(F/*&F,F1,&F)F)*$)F2F-F)F)F)*(F2F)F,F1,&F)F.F 7F)F)F5F9F97(F5F?*&F,F1,(F=F)*$)F7F-F)F)F)F)F)F?F5F97(F9F5F?FBF?F57(F9 F9F5F?F;F/7(F9F9F9F5F/F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*(%&sigm aG\"#7,&\"\"\"F(&%&alphaG6#\"\"#F(!\"\",.F(F-F)F(*$)&F*6#F(F,F(F(*&F)F (F0F(F(*$)F)F,F(F(*$)F)\"\"$F(F-F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 342 "f:=sqrt(1+alpha[2])*sqrt(1-alpha[2]-alpha[1]^2-alpha [2]*alpha[1]^2-alpha[2]^2+alpha[2]^3)\n/(2*Pi)^(n/2)/sigma^n*exp(-(x[1 ]^2+x[n]^2+(1+alpha[1]^2)*(x[2]^2+x[n-1]^2)+\n(1+alpha[1]^2+alpha[2]^2 )*sum(x[m]^2,m=3..n-2)-2*alpha[1]*(x[1]*x[2]+x[n-1]*x[n])\n+alpha[1]*( alpha[2]-1)*sum(x[m]*x[m-1],m=3..n-1)-alpha[2]*sum(x[m]*x[m-2],m=3..n) )/2/sigma^2);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"fG*,,&\"\"\"F'&%& alphaG6#\"\"#F'#F'F+,.F'F'*$)&F)6#F'F+F'!\"\"F(F2*&F(F'F/F'F2*$)F(F+F' F2*$)F(\"\"$F'F'F,),$*&F+F'%#PiGF'F',$*&F+F2%\"nGF'F'F2)%&sigmaGF?F2-% $expG6#,$*&#F'F+F'*&,0*$)&%\"xGF1F+F'F'*$)&FM6#F?F+F'F'*&,&F'F'F.F'F', &*$)&FMF*F+F'F'*$)&FM6#,&F?F'F'F2F+F'F'F'F'*&,(F.F'F4F'F'F'F'-%$sumG6$ *$)&FM6#%\"mGF+F'/F`o;F8,&F?F'F+F2F'F'*(F+F'F0F',&*&FLF'FWF'F'*&FZF'FP F'F'F'F2*(F0F',&F'F2F(F'F'-Fjn6$*&F^oF'&FM6#,&F`oF'F'F2F'/F`o;F8FfnF'F '*&F(F'-Fjn6$*&F^oF'&FM6#,&F`oF'F+F2F'/F`o;F8F?F'F2F'FA!\"#F'F2F'" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q3:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 23 "read\"Q3.m\": n:=nops(X):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "rho:=0:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 304 "for i to 4 do mu:=(X[1]+X[n]+(1-rho)*sum(X[j],j=2..n-1))/(n*(1- rho)+2*rho);\naux:=(1+rho^2)*sum((X[j]-mu)^2,j=2..n-1)-2*rho*sum((X[j] -mu)*(X[j+1]-mu),j=1..n-1)\n+(X[1]-mu)^2+(X[n]-mu)^2: sigma:=sqrt(aux/ n);\nrho:=(-sigma^2*rho/(1-rho^2)+sum((X[j]-mu)*(X[j+1]-mu),j=1..n-1)) /sum((X[j]-mu)^2,j=2..n-1)\nend do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#muG$\"+e,>C:!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$auxG$\"+D=p 7?!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG$\"+=&oM4(!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$rhoG$\"+9N_6&)!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"+[P\"G_\"!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$auxG$\"+Wj7Yb!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigma G$\"+mfhBP!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$rhoG$\"+HQC!\\)!# 5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"+%$auxG$\"+]t@Yb!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG$\"+%$rhoG$\"+J%#muG$\"+ !eNG_\"!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$auxG$\"+%f9ia&!\"'" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%&sigmaG$\"+!fXOs$!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$rhoG$\"+Snc!\\)!#5" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 2 "Q4" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "restart: read\"Q4.m\": N:=nops(X); xss:=add(X[i]^2 ,i=1..N):" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG\"%+5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "for i to 250 do r[i]:=sum(X[j]*X[j+ i],j=1..N-i)/xss end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "seq(r[i],i=1..50);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6T$!+!f,K?)!#5$\" +P'498&F%$!+'3>h#y!#6$!+(QAAN$F%$\"+:L#o8'F%$!+MO*z$oF%$\"+f4>IaF%$!+A -l)e#F%$!+(f93.(F*$\"+RGlfNF%$!+L1c'*\\F%$\"+m-!\\(\\F%$!+(G*=%[$F%$\" +pX(GC\"F%$\"+%[0a6\"F%$!+C2boGF%$\"+au.YNF%$!+TTRVJF%$\"+Dx8H=F%$!+a \")4!>*!#7$!+/1v[:F%$\"+d'HUb#F%$!+s*4Nx#F%$\"+)ob-?#F%$!+$=ISk*F*$!+] )[cx$F*$\"+D9'yb\"F%$!+\\%Hu>#F%$\"+un3>@F%$!+b\\nY:F%$\"+c_)4C&F*$\"+ gMUU^F*$!+=G*)o7F%$\"+8Qh0;F%$!+0c)fR\"F%$\"+vRPL%)F*$!+hFOcDFM$!+H7Db qF*$\"+`Hd\">\"F%$!+W\"zEK\"F%$\"+\"pBW2\"F%$!+VB&*pgF*$\"+(4I**o\"!#8 $\"+r;=7YF*$!+6Ng'o(F*$\"+71@\"H(F*$!+&p*>jXF*$\"+%40@b(FM$\"+y%fx&QF* $!+.t8TrF*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "with(plots): \+ 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