{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 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "G:=1-(1+x*60/12)*exp(-x*60/1 2):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "lambda:=13.2:" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "t:=.5: pt:=int(1-G,x=0..t)/t;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ptG$\"+C+ZAl!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "Lx:=t*pt*lambda:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "1-add(Lx^i/i!,i=0..5)*exp(-Lx);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"+HrSTE!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b )" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "Ly: =t*(1-pt)*lambda;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#LyG$\"+%yp^H#! \"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "1-add(Ly^i/i!,i=0..5 )*exp(-Ly);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*_o;(H!#5" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "Linf:=int(1-G,x=0..infinity)*lambda :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "1-add(Linf^i/i!,i=0..5 )*exp(-Linf);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+edXIV!#5" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q2" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "mu:=60/24.: ini:=3:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 68 "pt:=exp(-mu*0.5): PGF:=exp(lambda*(1-pt)/mu *(z-1))*(1-pt+pt*z)^ini:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "M:=eval(diff(PGF,z),z=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG$ \"+j!pni%!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "sqrt(eval( diff(PGF,z,z),z=1)+M-M^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+kx'H 4#!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "prob:=series(PGF,z,6):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "1-add(coeff(prob,z,i),i=0.. 5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+0!*)>;$!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 16 "Linf:=lambda/mu:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 35 "1-add(Linf^i/i!,i=0..5)*exp(-Linf);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+edXIV!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q3" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "A:=matrix(4,4,[-44,\01114,\01126,\0114,\n32,\011-59,\01119,\0118,\n20 ,\01135,\011-67,\01112,\n11,\01105,\01126,\011-42]/10);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&#!#A\"\"&#\"\"(F,#\"#8F,# \"\"#F,7&#\"#;F,#!#f\"#5#\"#>F8#\"\"%F,7&F2#F.F2#!#nF8#\"\"'F,7&#\"#6F 8#\"\"\"F2F/#!#@F," }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(li nalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names no rm and trace have been redefined and unprotected\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "s:=linsolve(transpose(A),[0,0,0,0]);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG-%'vectorG6#7&,$*&#\"%\\!*\"%GT \"\"\"&%#_tG6#F.F.F.,$*&#\"%\\mF-F.F/F.F.,$*&#\"%LB\"%w8F.F/F.F.F/" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "s:=evalm(s/add(s[i],i=1..4) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG-%'vectorG6#7&#\"%\\!*\"&D o##\"%\\mF+#\"%**pF+#\"%GTF+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b) " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "expo nential(A*25/60.)[2,3];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Fja\"\\ #!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "6.7*s[3]*24;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++j[&>%!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q4" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "lambda:=[3.3 ,\0114.1,\0110.9,\0111.3,\0112.5,\0111.9,\0110]:\nmu:=[2.3,\0113.0, \0114.1,\0110.8,\0111.2,\0112.3,\0110.2]:\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "w(0):=0: w(1):=sum(product(lambda[i],i=1..n-1)/pr oduct(mu[j],j=1..n),n=1..7):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "for j to 6 do w(j+1):=(1+mu[j]/lambda[j])*w(j)-mu[j]/lambda[j]*w (j-1)-1/lambda[j] end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"wG6# \"\"#$\"+fL\"\\_\"!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"wG6#\" \"$$\"+9zsX>!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"wG6#\"\"%$\"+ %)3m^P!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"wG6#\"\"&$\"+s63'y% !\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"wG6#\"\"'$\"+6HgU_!\")" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"wG6#\"\"($\"+7HgUd!\")" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "60/(.9+4.1); #minutes" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++++7!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q5" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "c:=7.3: d:=-5.2:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "with(stats): Pr:=z->statevalf[cdf,normald](z):" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "Pr((26-30-d*1.25)/sqrt(1.25*c));" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+R8`gz!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "t1:=-1.25: t:=0: t2:=19/60.: x1:=30: x2:=23:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "mu:=(t2*x1-t1*x2)/(t2-t1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"+h$*[TC!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "s:=sqrt(c*t2*(-t1)/(t2-t1));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG$\"+tB4e8!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "Pr((26-mu)/s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+,UE%y)!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q6 " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "s:=1 .35: a1:=1.2: a2:=-.7:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "l ambda:=solve(x^2-a1*x-a2,x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'l ambdaG6$^$$\"+++++g!#5$\"+&*=&4$eF)^$F'$!+&*=&4$eF)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 31 "This is why the model is stable" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "p:=abs(lambda[1]); \+ theta:=arctan(Im(lambda[1])/Re(lambda[1]));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"pG$\"+l-gm$)!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%&thetaG$\"+[]56x!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "ps i:=arctan((1+p^2)/(1-p^2)*tan(theta));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$psiG$\"+uo;\"R\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "r:=simplify(p^k*sin(k*theta+psi)/sin(psi));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"rG,$*&-%$expG6#,$%\"kG$!+?ZP$y\"!#5\"\"\"-%$sinG6#, &F+$\"+[]56xF.$\"+uo;\"R\"!\"*F/F/$\"+fJN;5F8" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "V=s^2*(1-a2)/(1+a2)/(1-a1-a2)/(1+a1-a2);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#/%\"VG$\"+$z8C7(!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "1-Pr((3-(2.3*a1-.4*a2))/s);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"+Fy==^!#5" }}}{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 55 "lambda:=7.4: mu:=7.7: ini:=4: ex:=exp(-(lambda-mu)*t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "pt:=(lambda-mu)*ex/(lambda-mu*ex):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "rt:=mu*(1-ex)/(lambda-mu*ex):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "PGF:=(rt+(1-rt)*pt*z/(1-(1-p t)*z))^ini:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "t:=0.25:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "M:=eval(diff(PGF,z),z=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"MG$\"+XR(4r$!\"*" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 36 "sqrt(eval(diff(PGF,z,z),z=1)+M-M^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+OfvtO!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "prob:=series(PGF,z,8):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "1-add(coeff(prob,z,i),i=0..7);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+!4)4B9!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c) " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "t:='t ';" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"tGF$" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 10 "F:=rt^ini:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "f:=diff(F,t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "int(t*f,t=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\" \"\"%)infinityG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "d)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "1-eval(F,t=4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*,(GWk!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q8" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 "Homogeneous:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "R:=exp(t); Q:=exp(int(cos(z),z));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>%\"RG-%$expG6#%\"tG" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"QG-%$expG6#-%$sinG6#%\"zG" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 27 "Any function of t + sin(z)" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 16 "Non-homogeneous:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "h:=exp(-int(tan(z),z)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG-%$cosG6#%\"zG" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "General solution:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "g(t+sin(z))*cos(z);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%\"gG6#,&%\"tG\"\"\"-%$sinG6#%\"zGF )F)-%$cosGF,F)" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 90 "Since at t=0 t his is cos(z)/sin(z), clearly g(..) is the reciprocal function. An swer:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "cos(z)/(t+sin(z)); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%$cosG6#%\"zG\"\"\",&%\"tGF(-%$ sinGF&F(!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q9" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(stats):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "c:=31.7: x0:=13.9: Pr:=z->1- statevalf[cdf,normald](z):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "1-Pr(- x0/sqrt(3*c));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*UfEq(!#5" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "1-2*Pr(x0/sqrt(3*c));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"+;\"o%f%)!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "%-(Pr((10.4-x0)/sqrt(c*3))-Pr((10.4+x0)/sqrt(c*3))); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+?,N@@!#5" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 2 "d)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "evalf(2/Pi*arccos(sqrt(3/4.25)));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"++c7\\O!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 " Q10" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "r estart:with(linalg):" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the prot ected names norm and trace have been redefined and unprotected\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 82 "P:=matrix(4,4,[-8,\0113,\011 0,\011-6,\n36,\011-15,\011-10,\01136,\n12,\011-6,\011-2,\01112,\n27, \011-11,\011-5,\01125]);\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG-% 'matrixG6#7&7&!\")\"\"$\"\"!!\"'7&\"#O!#:!#5F/7&\"#7F-!\"#F37&\"#F!#6! \"&\"#D" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "L:=eigenvalues(P );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"LG6&\"\"$\"\"\"!\"#F(" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "solve(\{seq(add(c(i)*L[i]^k, i=1..3)+c(4)*k*L[4]^(k-1)-P^k,k=0..3)\},\{seq(c(i),i=1..4)\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<&/-%\"cG6#\"\"%,*#\"\"#\"\"&\"\"\"*&# F-\"#:F-*$)%\"PG\"\"$F-F-F-*&#F+F0F-*$)F3F+F-F-!\"\"*&#F-F4F-F3F-F9/-F &6#F-,(#F+\"#DF9*&#F-\"#]F-F1F-F-*&#F4FDF-F7F-F-/-F&6#F+,*#F+F4F-*&#F- \"#=F-F1F-F9*&#F-FNF-F7F-F9*&#F(\"\"*F-F3F-F-/-F&6#F4,*#\"#J\"#vF-*&# \"\")\"$D#F-F1F-F-*&#F-FhnF-F7F-F9*&#F(FSF-F3F-F9" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 10 "assign(%):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "seq(evalm(c(i)),i=1..4);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&-%'matrixG6#7&7&\"\"!F(F(F(7&\"\"'!\"#F+F*F'7&\"\"$!\" \"F.F--F$6#7&7&F+\"\"\"F(F+7&\"\"#F.F(F57&\"\"%F+F(F7F6-F$6#7&7&F-F.F( F57&!\")F7F5F=7&!\"%F5F3F?7&!\"(F-F3!\"'-F$6#7&F'F'F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "evalm(add(c(i)*cos(L[i]*1.),i=1..3) -c(4)*sin(L[4]*1.));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7& 7&$!+@^/HB!\"*$\"+E9\\k&*!#5$\"\"!F/$!+&G)*G\">F*7&$!+uc " 0 "" {MPLTEXT 1 0 20 "exponential(P*I*1.):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q11" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "a1:=2.7: a2:=-2.59: a3: =0.873: s:=1.79:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "lambda :=solve(a3+a2*x+a1*x^2-x^3,x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%'l ambdaG6%$\"+++++!*!#5^$F&$\"+++++SF(^$F&$!+++++SF(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "abs(lambda[2]);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+-y&)[)*!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 12 " Yes, stable." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "r(0):=1:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "solve(\{ r(1)=a1+a2*r(1)+a3*r(2),r(2)=a1*r(1)+a2+a3*r(1)\},\{r(1),r(2)\});" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#<$/-%\"rG6#\"\"\"$\"+J9kB$*!#5/-F&6#\" \"#$\"+K3P8uF+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "assign(%) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "for k from 3 to 15 do \+ r(k):=a1*r(k-1)+a2*r(k-2)+a3*r(k-3) end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"rG6#\"\"$$\"*%*pyf%!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"rG6#\"\"%$\"+ft:`8!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"rG6#\"\"&$!+Nb3$y\"!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"rG6#\"\"'$!+Y!o]I%!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"rG6#\"\"($!+5e=Ce!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"rG6#\"\")$!+A\"4=8'!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> -%\"rG6#\"\"*$!+%yn&H_!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"rG6# \"#5$!+-;'HK$!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"rG6#\"#6$!*H^ [!y!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"rG6#\"#7$\"+E![P$>!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"rG6#\"#8$\"+v1jTV!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"rG6#\"#9$\"+:>jKg!#5" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>-%\"rG6#\"#:$\"+ZZWJn!#5" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 71 "V:=solve(V=V*(a1^2+a2^2+a3^2+2*(a1*a2+a2*a3)*r(1)+2 *a1*a3*r(2))+s^2,V);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"VG$\"+%R)) =\\#!\"'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(stats):" } }{PARA 7 "" 1 "" {TEXT -1 116 "Warning, these names have been redefine d: anova, describe, fit, importdata, random, statevalf, statplots, tra nsform\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "1-statevalf[cdf ,normald]((2.14+0.31*r(2))/sqrt(V*(1-r(2)^2)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+j'Q!=Z!#5" }}}}{MARK "76 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }