{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 }} {SECT 0 {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q1" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "P:=add(binomial(3,i-1)*z^i*. 4^(i-1)*.6^(4-i),i=1..4):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "mu:=eva l(diff(P,z),z=1); 3*.4+1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$ \"%+A!\"$" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#A!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "sqrt(eval(diff(P,z,z),z=1)+mu-mu^2) ; sqrt(3*.4*.6);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+u8G&[)!#5" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+u8G&[)!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "PP:=exp(-7.2*18/60*(1-P)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "mtaylor(PP,z,11);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,8$\"+57D`6!#5\"\"\"*&$\"+X)31Q&!#6F'%\"zGF'F'*&$\"+71k,7F&F')F,\" \"#F'F'*&$\"+w0,R7F&F')F,\"\"$F'F'*&$\"+r(=c6\"F&F')F,\"\"%F'F'*&$\"+B Sdu5F&F')F,\"\"&F'F'*&$\"+r)foE*F+F')F,\"\"'F'F'*&$\"+[hdNuF+F')F,\"\" (F'F'*&$\"+ZyHteF+F')F,\"\")F'F'*&$\"+tr5GWF+F')F,\"\"*F'F'*&$\"+_Lx-K F+F')F,\"#5F'F'" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "1-eval(% ,z=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*&[#=d'!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 12 "expand(P^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,0*&$\"&cm%!\"'\"\"\")%\"zG\"\"#F(F(*&$\"'Cm=F'F()F*\"\"$F(F(*&$ \"'S5JF'F()F*\"\"%F(F(*&$\"'![w#F'F()F*\"\"&F(F(*&$\"'S#Q\"F'F()F*\"\" 'F(F(*&$\"&ko$F'F()F*\"\"(F(F(*&$\"%'4%F'F()F*\"\")F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "1-coeff(%,z,2)-coeff(%,z,3);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"'?nw!\"'" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 2 "Q2" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "restart: A:=matrix(4,4,[0,21,35,10,9,0,23,18,33,11,0, 20,41,0,27,0]/10);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG 6#7&7&\"\"!#\"#@\"#5#\"\"(\"\"#\"\"\"7&#\"\"*F-F*#\"#BF-#F4\"\"&7&#\"# LF-#\"#6F-F*F07&#\"#TF-F*#\"#FF-F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "for i to 4 do A[i,i]:=-add(A[i,j],j=1..4) end do: eva lm(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&#!#L\"\"&#\" #@\"#5#\"\"(\"\"#\"\"\"7&#\"\"*F-!\"&#\"#BF-#F4F*7&#\"#LF-#\"#6F-#!#KF *F07&#\"#TF-\"\"!#\"#FF-#!#MF*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 " a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "wi th(linalg): linsolve(transpose(A),[0,0,0,0]);" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have been red efined and unprotected\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG 6#7&,$*&#\"&DS)\"&,Y&\"\"\"&%#_tG6#F,F,F,F-,$*&#\"&vx)F+F,F-F,F,,$*&# \"&EE&F+F,F-F,F," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "evalm(% /add(%[i],i=1..4));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'vectorG6#7&# \"&DS)\"'F!z##\"&,Y&F)#\"&vx)F)#\"%1D\"&(G8" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "exp(-13/60.*6.8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# $\"+FMg\"H#!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "exponential(A*1.,1 3/60.)[4,4];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+$yzn:$!#5" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "d)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "A:=mulrow(A,1,0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7&7&\"\"!F*F*F*7&#\"\"*\"#5!\"&#\" #BF.#F-\"\"&7&#\"#LF.#\"#6F.#!#KF3\"\"#7&#\"#TF.F*#\"#FF.#!#MF3" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "F:=exponential(A*1.,t)[4,1]; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG,**&$\"+:$GOg$!#5\"\"\"-%$ex pG6#,$*&$\"+TnRgi!\"*F*%\"tGF*!\"\"F*F4*&$\"*P+yI\"F)F*-F,6#,$*&$\"+;$ pa$*)F2F*F3F*F4F*F**&$\"+H<:FlF)F*-F,6#,$*&$\"+VR8/IF2F*F3F*F4F*F4$\"+ **********F)F*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "mu:=int(d iff(F,t)*t,t=0..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$ \"+4-rLF!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "sqrt(int(dif f(F,t)*(t-mu)^2,t=0..infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"+\\U7mH!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q3" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "Yes, since 1<1.3" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "restart : p:=1-1/1.3: L:=3.7: P:=(p/(1-(1-p)*z))^L:" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 37 "mu:=eval(diff(P,z),z=1); L*(1-p)/p;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"+LLLL7!\")" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"+LLLL7!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "sqrt(eval(diff(P,z,z),z=1)+mu-mu^2); sqrt((1-p)/p^2*L);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+P2d5t!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+K2d5t!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "coeff(mtaylor(P,z,11),z,10)*(3.7+10+1.3*10);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"+(e;Ch\"!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "pt:=(1-1.3)*exp(.3*10)/(1-1.3*exp(.3*10));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#ptG$\"+S7f*R#!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "rt:=1.3*(1-exp(.3*10))/(1-1.3*exp(.3*10));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#rtG$\"+&QJ0))*!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "PP:=(rt+(1-rt)*pt*z/(1-(1-pt)*z))^5*(pt/( 1-(1-pt)*z))^L:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "prob:=mt aylor(PP,z,8):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "1-eval(%, z=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Af`Eq!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q4" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 56 "restart: L:=n->1.04*(1.03^n-1): M:=n->1.03 *(1.04^n-1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "add(product (M(k)/L(k),k=1..n),n=0..100);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+q l:'3#\"#<" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 41 "clearly divergent; e xtinction is certain!" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "w[0]:=0: w[1]:=add(product(L(i)/M(i),i=1..n-1)/M(n) ,n=1..60);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"\"$\"+]sM%R %!\")" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "for i to 9 do w[i+ 1]:=(1+M(i)/L(i))*w[i]-M(i)/L(i)*w[i-1]-1/L(i) end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"#$\"+D4,#*p!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"$$\"+,gFg))!\")" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"%$\"+b\"*[J5!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"&$\"+?o%)\\6!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"'$\"+$*\\#*[7!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"($\"+8r`L8!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\")$\"+n$yoS\"!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"*$\"+&[)=r9!\"(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"#5$\"+CK5G:!\"(" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q5" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "restart: with(stats): P:=z->1-statevalf[cdf,normald]( z): c:=8.3:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "1-2*P(5/sqrt(c*2.5)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+oTRws!#5" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "P(-5/sqrt(c*2.5))-P(9/sqrt(c*2.5));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+u`G(R)!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "e valf(2/Pi*arccos(sqrt(2.5/4)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\" +nPp&>%!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "d)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "P((5-(-5+7*2.5/4))/sqr t(c*(2.5*1.5/4)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*A&R(=#!#5" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q6" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "restart:with(linalg):A:=matrix(4,4, [2,1,-5,-2,2,7,1,2,6,-1,13,2,-2,0,-2,6]);" }}{PARA 7 "" 1 "" {TEXT -1 80 "Warning, the protected names norm and trace have been redefined an d unprotected\n" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG-%'matrixG6#7 &7&\"\"#\"\"\"!\"&!\"#7&F*\"\"(F+F*7&\"\"'!\"\"\"#8F*7&F-\"\"!F-F1" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "eigenvalues(A);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6&\"\")\"\"'F#F$" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 118 "solve(\{C1+C2=1,\n6*C1+D1+8*C2+D2=A,\n6^2*C1+12*D1+8 ^2*C2+16*D2=A^2,\n6^3*C1+3*6^2*D1+8^3*C2+3*8^2*D2=A^3\},\{C1,C2,D1,D2 \}):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "assign(%): evalm(C 1); evalm(D1); evalm(C2); evalm(D2); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&\"\"\"#!\"\"\"\"##F(F+\"\"!7&F*F,F)F-F.7&F(F-F(F(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&!\"#\"\"!F(F(7&\"\"# F)F+F+F*7&F)F)F)F)" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7& \"\"!#\"\"\"\"\"##!\"\"F+F(7&F*F)F)F(7&F*F,#\"\"$F+F(7&F-F(F-F(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%'matrixG6#7&7&!\"#\"\"!F(F)F'7&\"\"# F)F+F)7&F)F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "evalm(C 1*ln(6.)+D1/6+C2*ln(8.)+D2/8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%'m atrixG6#7&7&$\"+MgU37!\"*$\"+?7TQ9!#5$!*(zursF*$!+7[LLLF-7&$\"+9`:5PF- $\"+J3gN>F*$\"+%4Wf,r)F*$!+?7TQ9F-$\"+\\nh1GF*F 97&$!+WC#o(GF-$\"\"!FFFC$\"+4(f " 0 "" {MPLTEXT 1 0 56 "restart: L:=n->piecewise(n<2,40.,n>2,40*.6^(n-2),40*. 8):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "M:=n->piecewise(n=0, 0,n=1,6.,12.):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "p:=[seq(p roduct(L(i-1)/M(i),i=1..n),n=0..20)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "p:=evalm(p/add(p[n],n=1..21));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"pG-%'vectorG6#77$\"+lA(4'>!#7$\"+V[J28!#6$\"+WhrdVF .$\"+Rw0i6!#5$\"+x_6CBF3$\"+K$Q*)y#F3$\"+*fN!3?F3$\"+*y8Zn)F.$\"+9e[[A F.$\"+R^%o\\$F+$\"+Nh(HE$!#8$\"+v*[o#=!#9$\"+N&4o8'!#;$\"+=!)*oB\"!#<$ \"+l)4e\\\"!#>$\"+J3N&3\"!#@$\"+N]9DZ!#C$\"+qMFM7!#E$\"+uhXM>!#H$\"+$ \\/\">=!#K$\"+T(yj-\"!#N" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "add((n- 2)*p[n+1],n=3..20);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+&QGo\"G!\"* " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "(p[2]+2*(1-p[1]-p[2]))/2;" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+NX-:**!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "2*6*%;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+WH!)*=\" !\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "d) in minutes:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "%%%/%*60;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#$\"+G[[?9!\")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 " Q8" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "re start: a:=(z^2-1)/z: b:=1/z:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "simplify(exp(-int(1/a,z)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&\"\"\"F$*&,&%\"zGF$F$!\"\"#F$\"\"#,&F'F$F$F$#F$F*F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "simplify(exp(-int(b/a,z)) );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&%\"zG\"\"\"F&F&F&,&F&F&*$)F% \"\"#F&!\"\"#F+F*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 73 "the general \+ solution is thus g[ exp(-t)/sqrt(1-z^2) ] (1+z)/sqrt(1-z^2)" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 94 "now: \+ g[ 1/sqrt(1-z^2) ] = 1/sqrt(1-z)/sqrt(1+z) which implies that g[x] = x" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "P:=exp(-t)/( 1-z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG*&-%$expG6#,$%\"tG!\"\" \"\"\",&F,F,%\"zGF+F+" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "si mplify(z*diff(P,t)+(1-z^2)*diff(P,z)-P);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "Q9" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 25 "P:=(add(z^i,i=1..6)/6)^4;" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"PG,$*&\"%'H\"!\"\",.%\"zG\"\"\"*$)F*\"\"#F+F+*$)F *\"\"$F+F+*$)F*\"\"%F+F+*$)F*\"\"&F+F+*$)F*\"\"'F+F+F4F+" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 16 "prob:=expand(P):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 41 "add(coeff(prob,z,i),i=10..24): evalf(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+yxxF!*!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "PP:=eval(P,z=.5+.5*z):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "mu:=eval(diff(PP,z),z=1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG$\"+++++q!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "sqrt(eval(diff(PP,z,z),z=1)+mu-mu^2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+ES6LD!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "prob:=expand(PP):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "add(coeff(prob,z,i),i=10..24);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+vL'pi\"!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q 10" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "re start: d:=5.72/1000:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "V:=4/3* Pi*8^3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "L:=evalf(V*d):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "1-add(L^i/i!,i=0..14)*exp (-L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+WO'p_#!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 14 "L:=4/3*Pi*x^3:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "F:=1-(1+L+L^2/2)*exp(-L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG,&\"\"\"F&*&,(F&F&*&#\"\"%\"\"$F&*&%#PiGF&)%\"xGF ,F&F&F&*&#\"\")\"\"*F&*&)F.\"\"#F&)F0\"\"'F&F&F&F&-%$expG6#,$**F+F&F,! \"\"F.F&F0F,F?F&F?" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "mu:=eva lf(int(x*diff(F,x),x=0..infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6 #>%#muG$\"+#*)frh)!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "sq rt(int((x-mu)^2*diff(F,x),x=0..infinity));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+z>Z; " 0 "" {MPLTEXT 1 0 53 "rest art: g:=piecewise(x<1,0,x<3,3/4*(1-(x-2)^2),0):" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 17 "G:=int(g,x=0..u):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "L:=4.3:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "p:=int ((1-G),u=0..2.5)/2.5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Lx :=p*2.5*L: Ly:=(1-p)*2.5*L:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "Lx^8/8!*exp(-Lx)*(1-add(Ly^i/i!,i=0..2)*exp(-Ly));" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"+?\"\\=W&!#6" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "Linf:=L*2; sqrt(Linf);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%LinfG$\"#')!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+gcdKH !\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "L*exp(-Linf)*24*365;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Pq*[$p!\"*" }}}}{MARK "73 0 1" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }