{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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q1" }{MPLTEXT 1 0 0 "" } {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "P:=matrix(4 ,4,[14,\01131,\01129,\01126,\n16,\01123,\01141,\01120,\n37,\01129,\011 15,\01119,\n24,\01109,\01152,\01115]/100);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG-%'matrixG6#7&7&#\"\"(\"#]#\"#J\"$+\"#\"#HF/#\"#8 F,7&#\"\"%\"#D#\"#BF/#\"#TF/#\"\"\"\"\"&7&#\"#PF/F0#\"\"$\"#?#\"#>F/7& #\"\"'F7#\"\"*F/#F3F7FB" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 " with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected n ames norm and trace have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 38 "s:=linsolve(transpose(P)-1,[0,0,0,0]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG-%'vectorG6#7&&%#_tG6#\"\"\",$*& #\"'*))G$\"'8nKF,F)F,F,,$*&#\"'e&Q%F1F,F)F,F,,$*&#\"'_`FF1F,F)F,F," }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "s:=evalm(s/add(s[i],i=1..4) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG-%'vectorG6#7&#\"'8nK\"(7& p8#\"'*))G$F+#\"&$4t\"'_#G##\"&t9\"\"&jq&" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "d:=[.22,.33,.08,.37];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"dG7&$\"#A!\"#$\"#LF($\"\")F($\"#PF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "evalm(d&*P^2)[3]*evalm(P^3)[3,1];" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"+U$G,V(!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "T:=submatrix(P,[1,3],[1,3]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% \"TG-%'matrixG6#7$7$#\"\"(\"#]#\"#H\"$+\"7$#\"#PF/#\"\"$\"#?" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "U:=submatrix(P,[1,3],[2,4]); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"UG-%'matrixG6#7$7$#\"#J\"$+\"# \"#8\"#]7$#\"#HF,#\"#>F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "evalm(inverse(1-T)&*U);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG 6#7$7$#\"$;$\"$n&#\"$^#F*7$#\"$J$F*#\"$O#F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "d[4]+d[1]*251/567+d[3]*236/567.;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+2$yo+&!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q2" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "F :=s->0.31+0.34*s+0.20*s^2+0.10*s^3+0.05*s^4;\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FGf*6#%\"sG6\"6$%)operatorG%&arrowGF(,,$\"#J!\"#\" \"\"*&$\"#MF/F09$F0F0*&$\"#?F/F0)F4\"\"#F0F0*&$\"#5F/F0)F4\"\"$F0F0*&$ \"\"&F/F0)F4\"\"%F0F0F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "ini:=5:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "x:=0: for i to 7 do x :=F(x) end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x^ini;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+,F-z')!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "x:=fsolve(s=F(s),s=0..0.99);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"xG$\"+h-M)e'!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "x^ini;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+o&48C\"! #5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "P:=s: for i to 7 do P:=F(P) end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "PGF:=P^ini:" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "mu:=eval(diff(PGF,s),s=1); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"+YL$QD#!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "sqrt(eval(diff(PGF,s,s),s=1)+mu-mu^ 2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+=]0g=!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "d)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "prob:=series(PGF,s,21):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "add(coeff(prob,s,i),i=10..20);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"+\\SeWD!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 " Q3" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "res tart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "solve(\{F0=p*s*F0+ q*s*F1,F1=p*s*F2+q*s*F1,F2=p*s*F0+q*s*F3,F3=p*s+q*s*F1\},\n\{F0,F1,F2, F3\}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "assign(%): " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "simplify(eval(F0-1/(1+(1-s)* (1+p*q*s^2)/p^2/q^2/s^4),q=1-p));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# \"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "PGF:=F0*F2^4: p:= 1/6.: q:=1-p:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "mu:=eval(d iff(PGF,s),s=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"+]++kE!\" (" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "sqrt(eval(diff(PGF,s,s ),s=1)+mu-mu^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+ " 0 "" {MPLTEXT 1 0 22 "restart: with(linalg):" }}{PARA 7 " " 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have b een redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "P:=matrix(5,5,[0,3,4,0,3,\n4,0,0,6,0,\n7,0,0,3,0,\n0,5,1,0,4, \n5,0,0,5,0]/10);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG-%'matrix G6#7'7'\"\"!#\"\"$\"#5#\"\"#\"\"&F*F+7'F.F*F*#F,F0F*7'#\"\"(F-F*F*F+F* 7'F*#\"\"\"F/#F8F-F*F.7'F7F*F*F7F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "f:=linsolve(transpose(P)-1,[0,0,0,0,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%'vectorG6#7',$*&#\"$q%\"$@$\"\"\"&%#_tG 6#F.F.F.,$*&#\"$A\"\"$2\"F.F/F.F.,$*&#\"$L#F-F.F/F.F.,$*&#\"$]\"F6F.F/ F.F.F/" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "f:=evalm(f/add(f[ i],i=1..5));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG-%'vectorG6#7'# \"#Z\"$%=#\"$$=\"$?*#\"$L#\"%S=#\"#XF+#\"$@$F1" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 18 "Pcap:=matrix(5,5):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 70 "for i to 5 do for j to 5 do Pcap[i,j]:=P[j,i]*f[j]/ f[i] end do end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "eval m(Pcap);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7'7'\"\"!#\"$m $\"%v6#\"%J;\"%+ZF(#\"$@$\"$S*7'#\"#Z\"$A\"F(F(#\"#vF5F(7'#\"$)=\"$L#F (F(#\"#XF;F(7'F(#\"#h\"$D\"#F;\"%+:F(#\"$2\"\"$+$7'#F4FEF(F(#\"#gFEF( " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "evalm(1.*Pcap^4)[5,2]; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+KQP))R!#5" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 2 "Q5" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "restart: ini:=4:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "F:=s->(((0.71-0.11*s)/(1-0.4*s)))^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FGf*6#%\"sG6\"6$%)operatorG%&arrowGF(*&,&$\"#r !\"#\"\"\"*&$\"#6F0F19$F1!\"\"\"\"#,&F1F1*&$\"\"%F6F1F5F1F6F0F(F(F(" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "H:=s: for j to 7 do H:=s*F(H) end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "PGF:= H^ini:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "mu:=eval(diff(PGF ,s),s=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"+>da]G!\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "sqrt(eval(diff(PGF,s,s),s=1) +mu-mu^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+ " 0 "" {MPLTEXT 1 0 48 "x[0]:=0: for j to 600 do x[j]:=F(x[ j-1]) end do:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "for n from 60 to 600 by 60 do n*x[n]^ini-add(x[k]^ini,k=0..n-1) end do;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*rPQ+*!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*luz/\"!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*v \"*z2\"!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"**z]$3\"!\"(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*CVW3\"!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*\\$f%3\"!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\" *&ph%3\"!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*@>Y3\"!\"(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*A>Y3\"!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*A>Y3\"!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "for n from 60 to 600 by 60 do n^2*x[n]^ini-add((2*k+1)*x[k]^ini, k=0..n-1) end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*V.h&=!\"'" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\")X<\"3$!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\")/@4N!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\")%R2 i$!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\")YBXO!\"&" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"(p+l$!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"(k4l$!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"(h5l$!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"(i5l$!\"%" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"(h5l$!\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "sqrt( 365.1061-10.8461922^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+#*e5t:! \")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "mu:=eval(diff(F(s),s),s=1): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "var:=eval(diff(F(s),s,s ),s=1)+mu-mu^2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "ini/(1-m u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+B+++7!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "sqrt(ini*var/(1-mu)^3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+T(pZR%!\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q6" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "p:=16/36.; q:=1-p: i:=1150/25; N:=(1150+275)/25;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"pG$\"+WWWWW!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%\"iG\"#Y" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"NG\"#d" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "w:=((q/p)^i-1)/((q/p)^N-1);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"wG$\"+')4m*e)!#6" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "tau:=(i-N*w)/(q-p);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$tauG$\"+*Q]$*p$!\"(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "sqrt(N/(q-p)*(4*(q/p)^i*tau/((q/p)^N-1)-3*N*w*(1-w)/( q-p))+4*p*q*tau/(q-p)^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+U%z8 \"=!\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q7" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "F:=(1/(1+(1-s)*(1+p*q*s^2)/p/q^2/s^3));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG*&\"\"\"F&,&F&F&*,,&F&F&%\"sG! \"\"F&,&F&F&*(%\"pGF&%\"qGF&)F*\"\"#F&F&F&F.F+F/!\"#F*!\"$F&F+" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "p:=1/6.: q:=1-p:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "mu:=coeff(series(F/(1-F)/(1-s),s,71 ),s,70);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"+FfNNp!\"*" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "sqrt(coeff(series(F*(1+F)/(1 -F)^2/(1-s),s,71),s,70)-mu^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+ F^R[>!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "add(coeff(seri es(F^k*(1-F)/(1-s),s,71),s,70),k=5..10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Q,,E')!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q8" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "restart : with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protecte d names norm and trace have been redefined and unprotected\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 148 "P:=matrix(6,6,[0,\0110,\011 12,\01188,\0110,\0110,\n0,\0110,\01131,\01169,\0110,\0110,\n44,\01156, \0110,\0110,\0110,\0110,\n91,\01109,\0110,\0110,\0110,\0110,\n24,\0110 5,\01106,\01111,\01124,\01130,\n18,\01106,\01102,\01110,\01141,\01123] /100):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "C1:=submatrix(P,[ 1,2],[3,4]):C2:=submatrix(P,[3,4],[1,2]):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 40 "s1:=linsolve(transpose(C1&*C2)-1,[0,0]):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 99 "s1:=evalm(s1/add(s1[i],i=1.. 2)); s2:=convert(evalm(s1&*C1),list);\n s1:=convert(evalm(s2&*C2),list );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s1G-%'vectorG6#7$#\"%Vw\"%2\" *#\"%k9F+" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s2G7$#\"%r8\"%2\"*#\"% OxF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#s1G7$#\"%Vw\"%2\"*#\"%k9F( " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "Pbar:=matrix(4,4,[0,1,0 ,0,1,0,0,0,6/25+1/20,17/100,6/25,3/10,12/50,6/50,41/100,23/100]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%PbarG-%'matrixG6#7&7&\"\"!\"\"\"F*F *7&F+F*F*F*7&#\"#H\"$+\"#\"# " 0 "" {MPLTEXT 1 0 20 "Pcap:=evalm(Pbar^2) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%PcapG-%'matrixG6#7&7&\"\"\"\" \"!F+F+7&F+F*F+F+7&#\"$z(\"%+D#\"$<*F0#\"$.*\"%+]#\"$T\"\"%+57&#\"%TH \"&++\"#\"%tLF<#\"%F>F<#\"%f " 0 "" {MPLTEXT 1 0 81 "Pabs:=evalm(inverse(1-submatrix(Pcap,[3,4],[3,4]))&*submatrix( Pcap,[3,4],[1,2]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%PabsG-%'matr ixG6#7$7$#\"$<(\"%e:#\"$T)F,7$#\"%r@\"%uY#\"%.DF2" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 151 "matrix(6,6,[op(s1),0,0,0,0,op(s1),0,0,0,0,0 ,0,op(s2),0,0,0,0,op(s2),0,0,\nop(s1*Pabs[1,1]),op(s2*Pabs[1,2]),0,0,o p(s1*Pabs[2,1]),op(s2)*Pabs[2,2],0,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7(7(#\"%Vw\"%2\"*#\"%k9F*\"\"!F-F-F-F'7(F-F-#\"%r8F* #\"%OxF*F-F-F.7(#\"(J+[&\")1()=9#\"'W[_\"(`V4(#\"(6I:\"F6#\"())HD$F9F- F-7(#\")`Hf;\")=hcU#\"'C(H&F9#\"(rQ9\"F6#\"(/;o*\")fIG@F-F-" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "evalm(%*1.);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7(7($\"+s`W#R)!#5$\"+GYb2;F*$\"\"!F.F- F-F-F'7(F-F-$\"+z`V0:F*$\"+@Yc%\\)F*F-F-F/7($\"+3'[A'QF*$\"+rI0)R(!#6$ \"+7!fi7)F9$\"+%=?`e%F*F-F-7($\"+*zf\")*QF*$\"+w,%oY(F9$\"+!eT=1)F9$\" +D?(*[XF*F-F-" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "evalm((P*1 .)^200);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7(7($\"+s`W#R) !#5$\"+GYb2;F*$\"\"!F.F-F-F-F'7(F-F-$\"+z`V0:F*$\"+@Yc%\\)F*F-F-F/7($ \"+3'[A'QF*$\"+rI0)R(!#6$\"+7!fi7)F9$\"+%=?`e%F*$\"+6/!zw\"!#c$\"+BS&3 \\\"F@7($\"+*zf\")*QF*$\"+w,%oY(F9$\"+!eT=1)F9$\"+D?(*[XF*$\"+)\\+v.#F @$\"+x_?= " 0 "" {MPLTEXT 1 0 28 "solve(9*x^3-15*x^2+7 *x-1,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6%\"\"\"#F#\"\"$F$" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "a:=i->c0*i+c1*i^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGf*6#%\"iG6\"6$%)operatorG%&arrowGF(,&* &%#c0G\"\"\"9$F/F/*&%#c1GF/)F0\"\"#F/F/F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "simplify(9*a(i+2)-15*a(i+1)+7*a(i)-a(i-1)-i);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#,**&\"\"%\"\"\"%#c0GF&F&*(\"\")F&%#c1 GF&%\"iGF&F&*&\"#?F&F*F&F&F+!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "solve(\{coeff(%,i,0),coeff(%,i,1)\},\{c0,c1\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<$/%#c0G#!\"&\"\")/%#c1G#\"\"\"F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "a:=i->A+B/3^i+C*i/3^i-5/8*i+ i^2/8;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"aGf*6#%\"iG6\"6$%)operat orG%&arrowGF(,,%\"AG\"\"\"*&%\"BGF.)\"\"$9$!\"\"F.*(%\"CGF.F3F.F1F4F.* &#\"\"&\"\")F.F3F.F4*&#F.F:F.*$)F3\"\"#F.F.F.F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "solve(\{a(0)=3,a(1)=-1,a(2)=0\},\{A,B,C\} );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#<%/%\"BG#!\"$\"#;/%\"CG#!#()\"\" )/%\"AG#\"#^F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "assign(%) : a(i);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,,#\"#^\"#;\"\"\"*(\"\"$F'F &!\"\")F)%\"iGF*F***\"#()F'\"\")F*F,F'F+F*F**(\"\"&F'F/F*F,F'F**&F/F*F ,\"\"#F'" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q10" }{MPLTEXT 1 0 0 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "F:=1/(1+(1-s)*(1+p*s+p^2*s^2+p^3*s^ 3+p^4*s^4)/p^5/s^5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG*&\"\"\" F&,&F&F&**,&F&F&%\"sG!\"\"F&,,F&F&*&%\"pGF&F*F&F&*&)F.\"\"#F&)F*F1F&F& *&)F.\"\"$F&)F*F5F&F&*&)F.\"\"%F&)F*F9F&F&F&F.!\"&F*F;F&F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "G:=1/(1+(1-s)*(1+q*s+q^2*s^2)/q^3/s ^3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"GG*&\"\"\"F&,&F&F&**,&F&F& %\"sG!\"\"F&,(F&F&*&%\"qGF&F*F&F&*&)F.\"\"#F&)F*F1F&F&F&F.!\"$F*F3F&F+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "p:=0.62: q:=1-p:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "X:=F*(1-G)/(1-F*G):limit(X,s =1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+/jjc^!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "H:=(F+G-2*F*G)/(1-F*G):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "mu:=limit(diff(H,s),s=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"+Bd`X8!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "sqrt(limit(diff(H,s,s),s=1)+mu-mu^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+-QBO5!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "prob:=series(H,s,10): add(coeff(prob,s,i),i=0..9);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Pu!og%!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q11" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning , the protected names norm and trace have been redefined and unprotect ed\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 107 "P:=matrix(6,6,[1,0 ,0,0,0,0,0,1,0,0,0,0,1/2,0,0,0,0,1/2,0,0,0,0,1,0,\n0,1/3,0,1/3,0,1/3, \+ 1/3,0,1/3,0,1/3,0]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG-%'matri xG6#7(7(\"\"\"\"\"!F+F+F+F+7(F+F*F+F+F+F+7(#F*\"\"#F+F+F+F+F.7(F+F+F+F +F*F+7(F+#F*\"\"$F+F2F+F27(F2F+F2F+F2F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "F:=inverse(1-submatrix(P,3..6,3..6));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG-%'matrixG6#7&7&#\"\"&\"\"%#\"\"\"\"\")#\"\" $F/#F1F,7&#F.F,#\"#8F/#\"#:F/F27&F4#F+F/F7F27&#F.\"\"#F4F2#F1F=" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "Pabs:=evalm(F&*submatrix(P,3 ..6,1..2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%PabsG-%'matrixG6#7&7 $#\"\"(\"\")#\"\"\"F,7$#\"\"$F,#\"\"&F,F/7$#F1\"\"%#F.F6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 32 "1/6+evalm([1,1,1,1]&*Pabs/6)[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6##\"\"*\"#;" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "tau:=evalm(F&*[1,1,1,1]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$ta uG-%'vectorG6#7&#\"\"&\"\"##\"\"*F+#\"\"(F+\"\"$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "mu:=evalm(tau&*[1,1,1,1]/6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG#\"\"*\"\"%" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "evalm((2*F&*tau-tau)&*[1,1,1,1]/6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "s qrt(%-mu^2.);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+ " 0 "" {MPLTEXT 1 0 26 "evalm([1,1,1,1]/6.&*F)[4];" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++++]i!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "122 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }