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4x5!#5$\"+g$[o;\"F/$\"+MMJo7F/$\"+2WC7IF/" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 23 "add(p[i]*(i-1),i=1..8);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+-Vc\\W!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "7.1*p[3]*60;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+2QeyS!\")" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q5:" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "restart: with(stats): c:=7.3:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "1-statevalf[cdf,normald[-3,s qrt(c*2.5)]](0);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+igi7C!#5" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "2*(1-statevalf[cdf,normald](3/sqrt( c*2.5)));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"*7__#[!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 76 "statevalf[cdf,normald](5/sqrt(c*2.5))-statev alf[cdf,normald](3/sqrt(c*2.5));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$ \"+c*[M?\"!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q6:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" }{MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "alpha1:=1.4: alpha2:=-0.8: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "1+alpha2; 1-alpha1-alp ha2; 1+alpha1-alpha2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"#!\"\" " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"\"%!\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"#K!\"\"" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 14 "(all positive)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b )" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "rho [0]:=1; rho[1]:=alpha1/(1-alpha2);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >&%$rhoG6#\"\"!\"\"\"" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$rhoG6#\" \"\"$\"+yxxxx!#5" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "for i f rom 2 to 10 do rho[i]:=alpha1*rho[i-1]+alpha2*rho[i-2] end do;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$rhoG6#\"\"#$\"**))))))G!\"*" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$rhoG6#\"\"$$!+wxxx@!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$rhoG6#\"\"%$!+)*****f`!#5" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#>&%$rhoG6#\"\"&$!+wxxhd!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$rhoG6#\"\"'$!+))))[yP!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$rhoG6#\"\"($!*AAY!o!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$rhoG6#\"\")$\"+**R9q?!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$rhoG6#\"\"*$\"+x8dUM!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%$rhoG6#\"#5$\"+HZ[jJ!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 48 "c) Normal, with mean 0 and standard deviation of" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "sqrt((1 -alpha2)/(1+alpha2)/(1-alpha1-alpha2)/(1+alpha1-alpha2))*2.1;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+,fYob!\"*" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "1-statevalf[cdf,normald[0,%]](5);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#$\"+t'eh%=!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q7:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a) " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "c:=6 : lambda:=31.4: mu:=60/(7+22/60.): rho:=lambda/mu:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "rho/c;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+q.PDk!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "G:=add( rho^i/i!,i=0..c-1)+rho^c/c!/(1-rho/c):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "rho^c/c!/G*rho/c/(1-rho/c)^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+2lR0X!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c) " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "add( rho^i/i!,i=0..c)/G;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+ " 0 "" {MPLTEXT 1 0 27 "1-add(rho^i/i!,i=0..c-1)/G; " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+u&*[1D!#5" }}}{EXCHG {PARA 0 " " 0 "" {TEXT -1 3 "Q8:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 19 "int(2*z/(z^2-1),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&-%#lnG6#,&%\"zG\"\"\"F)!\"\"F)-F%6#,&F(F)F)F)F)" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "simplify(exp(%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"zG\"\"#\"\"\"F(F(!\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "int(1/(1-z^2),z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%(arctanhG6#%\"zG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "simplify(exp(%));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# *&,&%\"zG\"\"\"F&F&F&,&F&F&*$)F%\"\"#F&!\"\"#F+F*" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 41 "P:=g((exp(t)*(1-z^2)))*(1+z)/sqrt(1-z^2);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG*(-%\"gG6#*&-%$expG6#%\"tG\"\" \",&F.F.*$)%\"zG\"\"#F.!\"\"F.F.,&F2F.F.F.F.F/#F4F3" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "P:=exp(t/2)*(1+z);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"PG*&-%$expG6#,$*&\"\"#!\"\"%\"tG\"\"\"F.F.,&%\"zGF. F.F.F." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 3 "Q9:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 68 "a) Since the sum of (3.4/3.2 )^k diverges, extinction is certain." }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "w[0]:=0:w[1]:=sum((3.2/3.4)^(n-1)/3.4/n^2,n=1..infini ty);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"\"$\"+l71 " 0 "" {MPLTEXT 1 0 72 "for i to 12 do w[i+1]:=(1+ 3.4/3.2)*w[i]-3.4/3.2*w[i-1]-1/3.2/i^2 end do;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"#$\"+f))=&)f!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"$$\"+EW2qo!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"%$\"+:J/ju!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"&$\"+U)fx*y!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"'$\"+gjkM#)!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"($\"+KFy0&)!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\")$\"+7'*3I()!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"\"*$\"+Uve>*)!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"#5$\"+])[B3*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"#6$\"+PF.C#*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"#7$\"+@au[$*!#5" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>&%\"wG6#\"#8$\"+e7bf%*!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 10 "c) Ignore" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q10:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 56 "a) lamda = 1.8 mu = 1/(2+3/24) * n M/M/infinity" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "pt:=exp(-t/(2+3/ 24)): P:=exp(1.8*(1-pt)*(2+3/24)*(z-1))*(1-pt+pt*z)^5:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 60 "prob:=series(eval(P,t=2.),z,5): add (coeff(prob,z,i),i=0..3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+B_R%e $!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "1.8*(2+3/24); sqrt(%);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"++++DQ!\"*" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+A2wb>!\"*" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "d) " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "exp( -1.8*(2+3/24))*1.8*365;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+97ZL9! \")" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 4 "Q11:" }{MPLTEXT 1 0 0 "" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "G:=x->piecewise(x<.5,0,x<.7 5,4*(x-.5),1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "pt:=int(1 -G(2-x),x=0..2)/2:" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 "a)" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "L:=16.1 *2*(1-pt): 1-add(L^i/i!,i=0..5)*exp(-L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+6H')****!#5" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 2 " b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "L: =16.1*2*pt: 1-add(L^i/i!,i=0..20)*exp(-L);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\")lf3 " 0 "" {MPLTEXT 1 0 20 "16.1*5 /8; sqrt(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+++D15!\")" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+&QW@<$!\"*" }}}}{MARK "99" 0 } {VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }