{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }} {SECT 0 {PARA 0 "" 0 "" {TEXT -1 31 "This is all the Maple syntax in" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 4 "" 0 "" {TEXT -1 31 "Chapter 2, Sections 2.5 and 2.6" }}{PARA 4 "" 0 "" {TEXT -1 75 "An Introducti on to the Mathematics of Biology, with Computer Algebra Models" }} {PARA 4 "" 0 "" {TEXT -1 34 "by Yeargers, Shonkwiler, & Herod. " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 34 "The Synta x is written for Maple 6." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restar t;" }}}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 25 "Exercises for Section 2.5 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "Exerc ise 1." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "with(linalg):\nA:= matrix([[0,0,-2],[1,2,1],[1,0,3]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eigenvects(A);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "J:=jordan(A,'Q');\nevalm(Q);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "P:=inverse(Q);\nevalm(P&*A&*inverse(P));" }}}{PARA 0 "" 0 "" {TEXT -1 11 "Exercise 2." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "with(linalg):\nC:=matrix([[-1,1,0],[1,-1,0],[0,0,-1]]);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "eigenvects(C);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "exptC:=exponential(C,t);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "U:=evalm(exptC&*[1,0,1]);" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "u:=unapply(U[1],t):\nv:=un apply(U[2],t):\nw:=unapply(U[3],t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "plot(\{u(t),v(t),w(t)\},t=0..1);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "Section 2.6" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "Page 54" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 239 "mcent:=[3.6, 3.7, 3.9, 4.3, 4.2, 4.0, 3.5, 2.9, 2.2, 2.0, 2.2, 2.1,\n 1.9,1.8,1.4, 0.8, 0.3]:\nfcent:=[3.6, 3.9 , 4.1, 4.7, 5.0, 4.3, 4.0, 3.6, 2.7, 2.8, 3.0, 3.1, \n 2.8, 2.3, 2.0, 1.7, 1.6]:\ntot:=[seq(mcent[i]+fcent[i],i=1..17)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 160 "ranges:=[0..5, 5..10, 10..15, 15.. 20, 20..25, 25..30, \n\011 30..35, 35..40, 40..45, 45..50, 50..5 5, 55..60, \n\011 60..65, 65..70, 70..75, 75..80, 80..85]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "with(stats): with(plots):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 149 "mpop:=[seq(Weight(ranges[ i],5*mcent[i]),i=1..17)]:\nfpop:=[seq(Weight(ranges[i],5*fcent[i]),i=1 ..17)]:\npop:=[seq(Weight(ranges[i],5*tot[i]),i=1..17)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 26 "statplots[histogram](pop);" }}} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "Page 55" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "age:=[2.5, 7.5, 12.5, 17.5 , 22.5, 27.5, 32.5, 37.5, 42.5, \n\011\01147.5, 52.5, 57.5, 62.5, 67.5 , 72.5, 77.5, 82.5];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "cu mmale:=[seq(sum('mcent[i]','i'=1..n),n=1..17)]:\ncumfale:=[seq(sum('fc ent[i]','i'=1..n),n=1..17)]:\ncumtot:=[seq(sum('tot[i]','i'=1..n),n=1. .17)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 124 "ptsm:=[seq([age[ i],cummale[i]],i=1..17)];\nptsf:=[seq([age[i],cumfale[i]],i=1..17)]:\n ptsT:=[seq([age[i],cumtot[i]],i=1..17)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "plot(\{ptsm,ptsf,ptsT\},color=BLACK);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 13 "Pages 56 & 57" }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "Sum('age[j]'*'tot[j]',j=1..17)=sum(age[j]*tot[j],\n\011\011j=1..17 );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "Sum('mcent[n]*age[n] ','n'=1..17)/Sum('mcent[n]','n'=1..17)\n\011= sum('mcent[n]*age[n]','n '=1..17)/sum('mcent[n]','n'=1..17);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "with(stats): with(describe):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "mean(pop); mean(mpop); mean(fpop);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "median(pop);median(mpop); median(fp op);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "P age 59" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "bus1:=[60,60,60,60]; bus2:=[30,0,120,90];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "range(bus1), range(bus2);\nmedian( bus1), median(bus2);\nmean(bus1), mean(bus2);\nvariance(bus1), varianc e(bus2);\nstandarddeviation(bus1), standarddeviation(bus2);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 235 "range(mpop), range(fpop), r ange(pop);\nmedian(mpop), median(fpop), median(pop);\nmean(mpop), mean (fpop), mean(pop);\nvariance(mpop), variance(fpop), variance(pop);\nst andarddeviation(mpop), standarddeviation(fpop), \nstandarddeviation(po p);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 7 "Pa ge 61" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "y:=(sigma,mu,x)->exp(-(x-mu)^2/(2*sigma^2))/\n\011(sq rt(2*Pi)*sigma);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "plot(\{ y(1,0,x),y(2,0,x),y(3,0,x)\},x=-10..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "plot(\{y(1,-4,x),y(1,0,x),y(1,4,x)\},x=-10..10);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 24 "Exercise for Section 2. 6" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 12 "Exer ecise 1." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "with(stats): wit h (plots): with(describe):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "Mort:=[1122.4, 55.1, 27.5, 33.4, 118.4, 139.6, 158.0, 196.4, 231. 0, \n\011287.8, 487.2, 711.2, 1116.9, 1685.1, 2435.5, 3632.4, 5300.0, \+ \n\0118142.0, 15278.0]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 " MortRate:=[seq(Mort[i]/100000,i=1..19)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "ranges:=[seq(5*i..5*(i+1),i=1..17)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "mortdata:=[Weight(0..1,MortRate[1] ), Weight(1..5,4*MortRate[2]),\n\011seq(Weight(ranges[i],5*MortRate[2+ i]),i=1..17)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "statplots [histogram](mortdata);" }}}{PARA 0 "" 0 "" {TEXT -1 16 "A Polynomial F it" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "xcord:=[seq(3+5*(i-1), i=1..18)];\nmortrate:=[seq(MortRate[i+1], i=1..18)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "plot([seq([xcord[i],mortrate[i]],i=1..18) ],style=POINT,symbol=CROSS);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "fit[leastsquare[[x,y],y=a+b*x+c*x^2+d*x^3]]([xcord,mortrate]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "approx:=unapply(rhs(%),x) ;\napprox(30)*100000;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "pl ot(approx(x),x=0..90);" }}}{PARA 0 "" 0 "" {TEXT -1 18 "An Exponential Fit" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "Lnmortrate:=map(ln,m ortrate);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "fit[leastsquar e[[x,y],y=m*x+b]]([xcord,Lnmortrate]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 40 "k:=op(1,op(1,rhs(%))); A:=op(2,rhs(%%));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "expfit:=t->exp(A)*exp(k*t);\nexpfit (30)*100000;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "J:=plot(ex pfit(t),t=0..85):\nK:=plot([seq([xcord[i],MortRate[i+1]],i=1..18)],\n \+ style=POINT,symbol=CROSS):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display(\{J,K\});" }}}{PARA 0 "" 0 "" {TEXT -1 32 "A Linear Sp line Fit for the Data" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "rea dlib(spline):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "linefit:=s pline(xcord,mortrate,x,linear):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "y:=unapply(linefit,x):\ny(30)*100000;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "J:=plot(y(t),t=0..85):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display(\{J,K\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "summary:=[Weight(Mort[1],1),Weight(Mort[2],4),\n \+ seq(Weight(Mort[i],5),i=3..19)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "range(summary); median(summary); mean(summary); \nsta ndarddeviation(summary);" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 " " 0 "" {TEXT -1 11 "Exercise 2." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "with(stats): with(plots): wi th(describe):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 182 "htinches: =[seq(60+i,i=1..15)];\nnumMales:=[0,0,0,0,0,2,1,2,7,10,14,7,5,2,1];\nr anges:=[seq(htinches[i]..htinches[i]+1,i=1..15)];\nmaledata:=[seq(Weig ht(ranges[i],numMales[i]),i=1..15)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "statplots[histogram](maledata);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "range(maledata); median(maledata); mean(maled ata); standarddeviation(maledata); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "`The average height is`,floor(%%/12),`feet and`,floor (frac(%%%/12)*12),`inches`;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "`The standard deviation is`, floor(frac(%%%/12)*12), `inches`;" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "mu:=mean(maledata); sigma:= standarddeviation(maledata);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "ND:=x->exp(-(x-mu)^2/(2*sigma^2))/(sigma*sqrt(2*Pi));" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "J:=plot(mu*ND(x),x=60..76): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "K:=statplots[histogram] (maledata):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plots[displa y](\{J,K\});" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 11 "Exercise 4." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "sigma:='sigma': mu:='mu':" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "f:=x->exp(-(x-mu)^2/(2*sigma ^2))/(sigma*sqrt(2*Pi));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "assume(sigma>0);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "int(x* f(x),x=-infinity..infinity);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "int((x-mu)^2*f(x),x=-infinity..infinity);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 11 "Section 2.7" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 8 "page 66." }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 28 "with(stats); with(describe);" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 12 "with(plots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "roll:=[seq(n,n=2..12)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "prob:=[1/36,2/36,3/36,4/36,5/36,6/36,5/36,4/36,3/36,2 /36,1/36];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "wtroll:=[seq( Weight(roll[i]-1/2...roll[i]+1/2,prob[i]),i=1..11)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "statplots[histogram](wtroll);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 8 "pag e 67." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "Sum('roll[i]*prob[i ]',i=1..11)=sum('roll[i]*prob[i]',i=1..11);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 74 "Sum('(roll[i]-7)^2*prob[i]',i=1..11)=sum('(roll[i] -7)^2*prob[i]',i=1..11);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "mean(wtroll);\nvariance(wtroll);" }}}{PARA 0 "" 0 "" {TEXT -1 8 "Page 68." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(combinat);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "permute([1,3,4]);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "numbperm(3);" }}}{PARA 0 "" 0 "" {TEXT -1 47 "page 69. There is more here than is on page 69." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(combinat);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "numbcomb(6,3);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 14 "binomial(6,3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "choose(6,3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "?choose" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "choose([a,b ,c,d,e,f],3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 7 "page 71" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "n:=60;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "flip:=[seq(b inomial(n,i)*(1/2)^i*(1-1/2)^(n-i),i=0..n)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "wthd:=[seq(Weight(i-1,flip[i]),i=1..n+1)]:" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "with(describe):\nmu:=mean(wt hd);\nsigma:=standarddeviation(wthd);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "G:=x->exp(-(x-mu)^2/(2*sigma^2))/(sigma*sqrt(2*Pi)); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "J:=plot(G(x),x=0..n):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "K:=statplots[histogram](w thd):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display(\{J,K\}); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 1 {PARA 3 "" 0 "" {TEXT -1 17 "Exercises for 2.7 " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Exerc ise 1" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(combinat):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "permute([a,b,c,d,e,f],3);\nnops(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "numbperm(6,3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "6!/3!;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(co mbinat):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "choose([a,b,c,d ,e,f],3);\nnops(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "numb comb(6,3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "6!/(3!*(6-3)! );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Exercise 2" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "with(combinat):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "numbcomb(5,3);\nnumbcomb(5,2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "numbperm(5,3);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Exercise 3" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(stats):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "die :=rand(1..6);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "for i from 1 to 6 do\n count[i]:=0:\nod:\ni:='i':" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 72 "for i from 1 to 300 do\n n:=die():\n count[n]:= count[n]+1:\nod:\ni:='i':" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "for i from 1 to 6 do\n print(count[i]);\nod;\ni:='i':" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Exercise 4" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "with(stats):\nwith(describe):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "red:=rand(1..6):\nblue:=rand(1..6): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "for i from 2 to 12 do\n count[i]:=0:\nod:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "for i from 1 to 360 do\n n:=red()+blue():\n count[n]:=count[n]+1:\nod :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "for i from 2 to 12 do \n print(count[i]);\nod;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "inter:=seq(n-1/2..n+1/2,n=2..12);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "throws:=[seq(Weight(inter[i-1],count[i]),i=2..12)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "mean(throws)=evalf(mean(t hrows));\nstandarddeviation(throws)=evalf(standarddeviation(throws)); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 238 "theory:=[Weight(inter[ 1],10),Weight(inter[2],20),Weight(inter[3],30),\n Weight(inter[4],40), Weight(inter[5],50),Weight(inter[6],60),\n Weight(inter[7],50),Weight( inter[8],40),Weight(inter[9],30),\n Weight(inter[10],20),Weight(inter[ 11],10)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "mu:=mean(theor y);\nsigma:=standarddeviation(theory);\nevalf(sigma);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "y:=x->360*exp(-(x-mu)^2/(2*sigma^2) )/(sigma*sqrt(2*Pi));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "J: =statplots[histogram](throws):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "K:=plot(y(x),x=0..14):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "plots[display](\{J,K\});" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 10 "Exercise 5" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 116 " binomial(2,0)*1/4*1/4;\nbinomial(2,1)*3/4*1/4;\nbinomial(2,2)*3/4*3/4; \nsum(binomial(2,j)*(3/4)^j*(1/4)^(2-j),j=0..2);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "binomial(5,2)*(3/4)^2*(1/4)^3;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "sum(binomial(5,j)*(3/4)^j*(1/4)^(5- j),j=2..5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{MARK "0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }