{VERSION 4 0 "IBM INTEL LINUX22" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 1 12 0 0 255 1 0 2 0 0 1 0 0 0 0 1 }{CSTYLE "" 0 21 "" 0 1 0 0 0 1 0 0 0 0 2 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Times" 1 14 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 3 0 3 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Times" 1 18 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 8 4 3 0 3 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Times " 1 14 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }1 1 0 0 4 4 1 0 1 0 2 2 0 1 } {PSTYLE "R3 Font 0" -1 256 1 {CSTYLE "" -1 -1 "Courier" 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 "R3 Font 2" -1 257 1 {CSTYLE "" -1 -1 "Times" 1 12 128 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 "Title" -1 258 1 {CSTYLE "" -1 -1 "Times" 1 36 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 12 12 3 0 3 0 2 2 19 1 }{PSTYLE "Normal" -1 259 1 {CSTYLE "" -1 -1 "Times" 1 16 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 1 0 1 0 2 2 0 1 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "restart; with(pldx): kernelopts(ASSERT=true): \n_EnvExplicit:=true: with(plots, display): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(gfun): " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 273 "n6:= 11 ; # le nombre de p ossibilit\351s dans le choix \351l\351mentaire.\nn := 119 ; # le nombr e d'essais dans une exp\351rience\nM := 853 ; # le nombre d'exp\351rie nces\nQx := nextprime(1656) ; # le nombre voulu de meta-exp\351riences # 1657\nis_fair:= false;\n_seed:= round(27182897*time()); " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 206 "displayg:= proc()\nglobal d isplay;\noption `Copyright Pierre L. Douillet`;\n display(args, 'font' = ['TIMES', 'ROMAN', 16], 'labelfont' = ['TIMES', 'ROMAN', 16],\n 'ax esfont' = ['TIMES', 'ROMAN', 16])\nend proc;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Configuration et alias" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "if kernelopts(platform)=\"unix\" \n the n ici_0:= \"docs/Cherche/chi2/\" else ici_0:= \"f:/docs/Cherche/chi2/ \" \nfi:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 172 "if is_fair then \n ic i:= \"\"||(ici_0)||\"fair/\";\n alias(r=r_fair, th=th_fair);\nelse\n \+ ici:= \"\"||(ici_0)||\"unfair/\";\n alias(r=r_unfair, th=th_unfair, \+ prop=prop_unfair); \nfi;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "ifactor(n), ifactor(M), ifactor(Qx); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "mem_warn:= interface(warnlevel): interface(warnlevel =0): \nwith(stats): with(describe): with(statplots, histogram): inter face(warnlevel=mem_warn):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 162 "chi2:= (nu,t)->stats[statevalf,pdf,chisquare[nu]](t):\nChi2:= (nu ,t)->stats[statevalf,cdf,chisquare[nu]](t):\nIChi:= (nu,t)->stats[stat evalf,icdf,chisquare[nu]](t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 408 "chi2:= (nu,t)->`stats/statevalf/pdf/functions/chisquare`(t,nu); \nChi2:= (nu,t)->`stats/statevalf/cdf/functions/chisquare`(t,nu);\nICh i:= (nu,t)->`stats/statevalf/icdf/functions/chisquare`(t,nu);\ngauss:= t->stats[statevalf,pdf,normald](t):\nnorlaw:= (m,s,t)->stats[stateval f,pdf,normald[m,s]](t):\nCnorlaw:= (m,s,t)->stats[statevalf,cdf,normal d[m,s]](t):\nICnorlaw:= (m,s,t)->stats[statevalf,icdf,normald[m,s]](t) :" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 203 "for nuu in [$2..9, seq (10*k, k=1..10), seq(100*k, k=1..10)] do \n try 1-Chi2(nuu, nuu+2*sqrt (2*nuu)) + Chi2(nuu, nuu-2*sqrt(2*nuu));\n catch : 1-Chi2(nuu, nuu+2*s qrt(2*nuu));\n end try;\nASSERT(%<0.05); \nod;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 17 "A pro pos du chi^2" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 39 "recurrence sur l' esperance du chisquare" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "k: ='k': q:='q': \nexp1:= pr(i,k,l)*((i-N*p)^2/(N*p)+(k-N*r)^2/(N*r)+(l-N *s)^2/(N*s));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "(j-N*q)^2 /(N*q): selectremove(has,op(2, exp1),i):\nexp2:= subsop(2=%[1]+%%,exp1 )+subsop(2=%[2]-%%,exp1);\n(ASSERT@expand)(exp1=exp2);\n " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "(k-N*r)^2/(N*r)+(l-N*s)^2/(N*s)-(j- N*q)^2/(N*q);\nsubs(N=j/q, %); " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 " exp3:= %%=``(factor(subs(r=q-s, l=j-k, %%/%)))*%;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 150 "subs(k=j,l=NULL,pr(i,j)=``(N!/i!/j!*p^i*q^j ),remove(has,exp2,N*s));\nSum(%, i=0..N); (factor@xcombipo@expand@valu e@xjoli@expand@subs)(j=N-i, p=1-q, %);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 4 "nu=1" }} {EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 172 "tmp:= N!*p^i*q^j/i!/j!*((i-N *p)^2/(N*p)+(j-N*q)^2/(N*q)):\ncollect(subs(j=N-i, %), [i], normal):\n value(xjoli(Sum(%,i=0..N))):\nE((chi^2)[1])=(xcombipo@expand@subs)(p=1 -q, %);" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 279 "tmp:= N!*p^i*q^j /i!/j!*((i-N*p)^2/(N*p)+(j-N*q)^2/(N*q))^2 :\ncollect(subs(j=N-i, %), \+ [i], normal):\nvalue(xjoli(Sum(%,i=0..N))):\ntoto:= collect((xcombipo@ expand@subs)(p=1-q, %), N, factor):\np*q=(1-q)*q: solve(expand(%), \{q ^2\}): var((chi^2)[1])=collect(subs(%, q-1=-p, toto)-1, N);" }}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 4 "nu=2" }}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 424 "tmp:= N!*p^i*q^j*r^k/i!/j!/k!*((i-N*p)^2/(N*p)+(j-N *q)^2/(N*q)+(k-N*r)^2/(N*r)):\ncollect(subs(k=N-i-j, %), [i,j], normal ):\nvalue(xjoli(Sum(%,j=0..N-i))): \n(expand@yjoli@subs)( seq(((r+q)/r )^(N-i-u)=(r+q)^(N-i-u)/(r)^(N-i-u), u=0..1), %):\nvalue(xjoli(Sum(col lect(%, i, factor), i=0..N))):\n(expand@yjoli@subs)( seq(((p+r+q)/(r+q ))^(N-u)=(p+r+q)^(N-u)/(r+q)^(N-u), u=0..1), %):\nE((chi^2)[2])=(xcomb ipo@expand@subs)(p=1-q-r, %);" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 417 "tmp:= N!*p^i*q^j*r^k/i!/j!/k!*((i-N*p)^2/(N*p)+(j-N*q)^2/(N*q) +(k-N*r)^2/(N*r))^2:\ncollect(subs(k=N-i-j, %), [j], normal):\nvalue(x joli(Sum(%,j=0..N-i))): \n(expand@yjoli@subs)( seq(((r+q)/r)^(N-i-u)=( r+q)^(N-i-u)/(r)^(N-i-u), u=0..1), %):\nvalue(xjoli(Sum(collect(%, i, \+ factor), i=0..N))):\n(expand@yjoli@subs)( seq(((p+r+q)/(r+q))^(N-u)=(p +r+q)^(N-u)/(r+q)^(N-u), u=0..1), %):\ntoto:= (xcombipo@expand@subs)(p =1-q-r, %);" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 251 "collect(toto , N, factor): (normal@subs)(r+q-1=p, solve(expand((1-q-r)*q*r=p*q*r), \{q^2\}), %):\ncollect(%,N, factor): subs(solve(expand((1-q-r)*q*r)=p* q*r,\{r^2\}), %):\nvar((chi^2)[2])=collect(%-4,N, expand);\nexemple= s ubs(r=1-p-q, p=0.1, q=0.1, N=100, %);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 4 "nu=3" }}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 355 "jj:=4: p chi:= N!*mul(p[j]^i[j]/i[j]!, j=1..jj)*add( (i[j]-N*p[j])^2/(N*p[j]), \+ j=1..jj);\nsubs(i[4]=N-i-j-k, i[3]=k,i[2]=j,i[1]=i, p[3]=q, p[4]=r, p[ 1]=s, p[2]=p, pchi):\nmap(collect,%,[i,j,k], factor):\nxjoli(Sum(expan d(%),k=0..N-i-j)): valx:= value(%):\nxjoli(Sum(expand(valx), j=0..N-i )): valy:= value(%):\nxjoli(Sum(expand(valy), i=0..N)): valz:= value(% ):" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 269 "tmp:= subs( seq(((s+p +r+q)/(p+r+q))^(N-u)=((s+p+r+q))^(N-u)/((p+r+q))^(N-u),u=0..2), seq((( p+r+q)/(r+q))^(N-u)=((p+r+q))^(N-u)/((r+q))^(N-u),u=0..2), \nseq(((r+q )/(r))^(N-u)=((r+q))^(N-u)/((r))^(N-u),u=0..3), valz):\nsubs(s=1-p-q-r , expand(tmp)): E((chi^2)[3])=normal(%);" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 24 "la variance ne sort pas " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 39 "La varianc e de l'estimateur de variance" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "jj:=13: val_S2:= Sum(x[j]^2, j=1..J)/J- Sum(x[j], j=1..J)^2/J^2; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 454 "E:= proc()\nlocal theA rgs, arg, look, cf, term;\n theArgs := args;\n arg := args[1];\n if ar g = 1 then return 1\n elif type(arg, 'name') then\n elif type(arg, 'co nstant') then return arg*procname(1, args[2 .. -1]);\n elif type(arg, \+ '`+`') then return map(procname, args);\n elif type(arg, '`*`') then r eturn map(procname, args);\n fi;\n 'procname'(theArgs)\nend proc: \nas sign( seq(E(x[j])=0, j=1..jj), seq(E(x[j]^2)=sigma^2, j=1..jj), seq(E( x[j]^4)=mu4, j=1..jj) );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "tmp:= [seq(map(E, expand(value(val_S2)^2)) -((J-1)/J*sigma^2)^2 , J=1 ..13)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "[0,seq(coeff(tm p[J],mu4)*J^3, J=1..13)]; factor(guessgf(%, z)[1]): \ncoe_mu4:= factor (ratpolytocoeff(%, z, J)): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 206 "[0 ,seq(coeff(tmp[J],sigma,4)*J^3, J=1..13)]; \nfactor(guessgf(%, z)[1]): coe_sig4:= factor(ratpolytocoeff(%, z, J)):\nformule_variance_predict eur_s2:= collect((coe_mu4*mu4+coe_sig4*sigma^4)/J/(J-1)^2, [mu4]);" }} }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 31 "Pourquoi la granularit\351 de c hi2" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 162 "vv:= seq(Y[k],k=1..n6-1), n-add(Y[k], k=1..n 6-1); th:= [seq(n/n6,k=1..n6)];\ntmp:= add((th[k]-vv[k])^2/th[k], k=1. .n6):\nxcs(expand(%), vv[1]): select(has,%, Y[1]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 84 "'(n6-1)*n^2', (n6-1)*n^2, (eval@subs)(Y=[n, 0$(n6-1)], tmp)*n; tau:= modp(%[3],2*n6);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 89 "fu := proc (z) options operator, arrow; (2*round(1/2* (n*z-tau)/n6)*n6+tau+n6)/n end proc;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "m:=6: th:= [seq(1/(m+1),k=1..m-1),2/(m+1)];" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 214 "m:=6: vv:= seq(Y[k],k=1..m-1), 1-add(Y[k ], k=1..m-1); th:= [seq(2*k/m/(m+1),k=1..m)];\nadd(th[k],k=1..m); \nad d((th[k]-vv[k])^2/th[k], k=1..m):\nseq( remove(has,select(has,xcs(expa nd(%), Y[k]),Y[k]),Y[k]), k=1..m-1);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "(n/n6-n)^2/(n/n6);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 32 "loi de la variance d'\351chantillon" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 62 "f_chi:= (nu,y)-> exp(-y/2)*(y/2)^(nu/2-1)*1/2* 1/GAMMA(1/2*nu);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "gu:= un apply(f_chi(nu, nu*s2/sigma2)*nu/sigma2, s2, sigma2, nu);\n" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 137 "Int(z*gu(z, sigma^2, nu),z= 0..infinity): student[changevar](z=sigma^2*u/nu,%,u):\nsubs(signum(sig ma)=1, signum(nu)=1,%): normal(value(%));" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 150 "Int(z^2*gu(z, sigma^2, nu),z=0..infinity): student [changevar](z=sigma^2*u/nu,%,u):\nsubs(signum(sigma)=1, signum(nu)=1,% ): value(%); normal(%-sigma^4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 117 "gu:= unapply(chi2(nu, nu*s2/sigma2)*nu/sigma2, s2, sigma2, nu );\nGu:= unapply(Chi2(nu, nu*s2/sigma2), s2, sigma2, nu);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 15 "Stats revisited" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "` pldx/islessequal`:= proc(a,b); `stats/islessequal`(a,b); \nif member(% , \{true, false\}) then return % else error \"can't compare \",a,b fi; end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 936 "`pldx/tally`:= \n proc(data, topname) global tally_table; local count, item, value;\nopt ion `Copyright (c) 1993 by Waterloo Maple Inc. All rights reserved.`; \n if nargs <> 2 then RETURN(`stats/abort`(topname, [topname, `Incorre ct number of arguments`], [args]))\n end if;\n if not type(data, `stat s/data`) then\n RETURN(`stats/abort`(topname, [topname, `requires dat a of type stats/data, received`, data], [args]))\n end if;\n tally_tab le := table();\n for item in data do\n if type(item, function) and op (0, item) = 'Weight' then value := op(1, item); count := op(2, item)\n else value := item; count := 1\n end if;\n if assigned(tally_table [value]) then tally_table[value] := tally_table[value] + count\n else tally_table[value] := count\n end if\n end do;\nmap(Weight@op, (op@e val)(tally_table));\ntry sort(%, `pldx/islessequal`);\ncatch : %\nend \+ try \nend;\ntransform[tally]([red,blue,red]):\n`stats/transform/funct ions/tally`:= eval(`pldx/tally`):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 692 "cut_n:= proc(li_,n) local li,j,M,res,yet, oldyet,bas e,base2,k,top;\nli:= transform[tally](li_); M:= count(li); res:= array (1..n);\nj:=1; top:= M/n; oldyet:=0; yet:=0; \nop(1,li[1]); base:= `if `(type(%,range),lhs(%),%);\nfor k from 1 to nops(li) do yet:=yet+op(2, li[k]);\nif yet >= top then \n base2:= op(1,li[k]); if type(base2,rang e) then base2:= rhs(base2)\n elif j " 0 "" {MPLTEXT 1 0 1256 "histo:= proc(tallied) local jx, j, x, y, r, numpolys, numlines , polys, lines, \n others, plotargs, xrange_, area_, sel, opt;\nother s:= select(type,[args[2..-1]],`=`); plotargs:=NULL;\njx:= nops(tallied );\n\nopt:= proc(nom, var, defaut); sel:= select(has,others,nom); \nif sel=[] then var:= defaut; \n else var:= subs(sel,nom); others:= remo ve(has,others,nom);\nfi; NULL; end; \n\nrange(tallied); (rhs-lhs)(%)/j x; lhs(%%)-%..rhs(%%)+%;\nopt(xrange, xrange_, %); plotargs:= plotargs , view=[xrange_,DEFAULT];\n\ncount(tallied); opt(area, area_, %); area _:= area_/%; \n\npolys:= array(1..jx); lines:= array(1..jx);\nnumpolys :=0; numlines:=0;\n for j to jx do\n if type(tallied[j], function) \+ and op(0, tallied[j]) = 'Weight' then\n x := op(1, tallied[j]); y : = op(2, tallied[j])\n else x := tallied[j]; y := 1\n end if;\n i f type(x, range) then\n numpolys := numpolys + 1; r := op(2, x) - o p(1, x);\n if r =0 \n then polys[numpolys] := NULL\n else p olys[numpolys] := [x, 0 .. y/r*area_]\n fi;\n else\n numlines \+ := numlines + 1; lines[numlines] := [x, 0 .. y]\n end if\n end do; \+ \n display(\n `stats/statplots/plotformat`([], convert(lines, list)[ 1 .. numlines], convert(polys, list)[1 .. numpolys]),\n color=xcolor( fill), op(others), plotargs)\nend proc:" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "divi:= 999999999989: Digits:=20: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 219 "r_unfair := proc () local k; global _seed, n6; _seed := irem(427419669081*_seed,999999999989); \ndo k:= irem(_se ed, n6)+1; \n _seed := irem(427419669081*_seed,999999999989); \n if _s eed < prop[k] then return k fi;\nod;\nend:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 7 "M\351thode" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 303 "prop_unfair:= seq(3.+rand()/divi ,k=1..n6): floor(divi/max(prop_unfair))*[prop_unfair]: \nprop_unfair:= map(floor,%); ASSERT((max@op)(prop_unfair) \+ " 0 "" {MPLTEXT 1 0 468 "prop_unfair := [898098513398, 841410946514, 9 17791186570, 947375991524, 957485498182, 999999999987, 820283943877, 8 24900920837, 974525206305, 955478558949, 847175665499];\nth_unfair := \+ [10.703935116608844365, 10.028307633885397894, 10.938641101265405866, \+ 11.291245885641445916, 11.411735455230792592, 11.918442082674012021, 9 .7765066765725388577, 9.8315338490680545396, 11.614822229603078120, 11 .387815866218524933, 10.097014103231904895];\nASSERT(add(k,k=th_unfair )=n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "r_fair:= proc () local k; global _seed, \+ n6; _seed := irem(427419669081*_seed,999999999989); \nk:= irem(_seed, \+ n6)+1; \nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "th_fair:= \+ seq(n/n6*1.,k=1..n6);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 " " {TEXT -1 15 "For a fair dice" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "m ea_th:= add(k, k=1..n6)/n6*1.; var_th:= add(k^2, k=1..n6)/n6-%^2;" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 27 "For the present unfair dice" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "add(th[k],k=1..n6)/n; mea_th:= add( k*th[k],k=1..n6)/n; var_th:= add(k^2*th[k],k=1..n6)/n-%^2;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "mu4_th:= add((k-mea_th)^4*th[k],k=1..n6)/n; " }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 20 "Lets have an example" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "li:=sort( ['r'()$n]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 168 "X:=[seq(nops(select(has,li,k)), k=1..n6)];\n mea_m:= add(k*X[k], k=1..n6)/n*1.;\nvar_m:= (add(k^2*X[k], k=1..n6)-%^ 2*n)/(n-1);\nm_chi_m:= add((X[k]-th[k])^2/th[k],k=1..n6);" }}{PARA 0 " > " 0 "" {MPLTEXT 1 0 67 "[seq(Weight(k-1/2..k+1/2,X[k]), k=1..n6)]: p l1:= histo(%, area=1):;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "[seq(Wei ght(k-1/2..k+1/2,th[k]), k=1..n6)]: pl2:= histo(%, area=1, color=yello w):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "displayf(pl1,pl2, tickmarks= [[1,6,11],[0.09]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 21 "Missing day (why ???)" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 17 "T\351l\351charg\351s (???)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 377 "m_mea:=array[1..M] : m_var:=array[1..M]: m_chi:=array[1..M]:\nmem_seed:=731025457871; _se ed:= %;\n for m to M do li:=sort( [ 'r'()$n]):\n X:=[seq(nops(select(h as,li,k)), k=1..n6)];\n m_mea[m]:= add(k*X[k], k=1..n6)/n*1.;\n m_var[ m]:= add(k^2*X[k], k=1..n6)/(n-1)-%^2*n/(n-1);\n m_chi[m]:= add((X[k]- th[k])^2/th[k],k=1..n6);\n od: \n cat(ici, mem_seed); save n6,n,M,m_me a,m_var,m_chi, %;" }}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 79 "for qzq to Q do if table_seed[qzq]=731025457871 then print (qzq) ; break fi o d;" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 9 "Many days" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "_seed; name_seed:= cat(ici,\".seed\");" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 144 "try read name_seed;\ncatch : tabl e_seed:= table(): Q:=0; save table_seed, _seed, Q, name_seed; \nend tr y; deja_traites=Q; ASSERT(Q<=Qx, `bad Qx`);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 502 "m_mea:=array[1..M]: m_var:=array[1..M]: m_chi:=array [1..M]:\nstamp:=time(): for qzq from Q+1 to Qx \ndo mem_seed:=_seed;\n for m to M do li:=sort( [ 'r'()$n]):\n X:=[seq(nops(select(has,li,k)) , k=1..n6)];\n m_mea[m]:= add(k*X[k], k=1..n6)/n*1.;\n m_var[m]:= add( k^2*X[k], k=1..n6)/(n-1)-%^2*n/(n-1);\n m_chi[m]:= add((X[k]-th[k])^2/ th[k],k=1..n6);\n od: \n cat(ici, mem_seed); save n6,n,M,m_mea,m_var,m _chi, %;\n table_seed[qzq]:= mem_seed;\nod: \nQ:= Qx; save table_seed, _seed, Q, name_seed;\nlaps:= time()-stamp;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 175 "n*M*Q: round(%/10^6)* millions_d_evenements;\nvitess e = round(%%/laps) *evenements_par_seconde;\n# 166*millions_d_evenemen ts\n# vitesse = 23741*evenements_par_seconde\n# laps 7084" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "read ca t(ici,\".seed\"):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "read c at(ici, table_seed[1]):" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 64 "Progr ammes de traitement d'un jour donn\351 (M batches de taille n)" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "cut:=21; cut2:= 16;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 398 "test_law:= proc(li, loi, Q) # liste, repart, taille\nglobal tmp; local ran; ran:=range(li);\n A SSERT( lhs(op(1,li[1]))=lhs(ran)); \n ASSERT( rhs(op(1,li[-1]))=rhs(ra n));\n subsop([1,1,1]=.0001, [-1,1,2]=1000., li); map(convert, %, list );\n tmp := [seq([loi(rhs(k[1])) - loi(lhs(k[1])), 1.*k[2]/Q], k = %)] ;\n add((k[1] - k[2])^2/k[1], k = %)*Q;\n evalf((% - nops(tmp) + 1)/sq rt(2*nops(tmp) - 2), 5)\nend:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 330 "test_law_chi:= proc(li, loi, Q) global tmp; local ran; ran:=ra nge(li);\n ASSERT( lhs(op(1,li[1]))=lhs(ran)); \n ASSERT( rhs(op(1,li[ -1]))=rhs(ran));\n subsop([1,1,1]=.0001, [-1,1,2]=1000., li); map(conv ert, %, list);\n tmp := [seq([loi(rhs(k[1])) - loi(lhs(k[1])), 1.*k[2] /Q], k = %)];\n add((k[1] - k[2])^2/k[1], k = %)*Q;\nend proc :" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 190 "proc(li, loi, Q) global tmp; # liste, repart, tail le\nmap(convert,li,list):\ntmp:= [seq( [loi(rhs(k[1]))- loi(lhs(k[1])) , k[2]/Q*1.], k=%)]:\nadd( (k[1]-k[2])^2/k[1], k=%)*Q; # print(%); \n end:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 32 "meab : equ(21), par(21), par(16)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 152 "law_meab:= t->norlaw(mea_th, sqrt( var_th/n), t); \nLaw_meab:= t->Cnorlaw(mea_th, sqrt(var_th/n), t):\npm 0:= plot(law_meab(t), t=4.5..7.5, linestyle=24): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "fac:=9: ran:= 5..64/9: floor(op(1,%)*fac). .floor(op(2,%)*fac-1):\nequ_meab:= [0..5, seq(k/fac..(k+1)/fac,k=%), 6 4/9..100]; nops(%);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 186 "[ seq(5.+rand()/divi, k=1..cut)]: %/add(k,k=%):\n[seq(add(%[j],j=1..k),k =1..cut-1)]:\n[0, (op@map)(t->ICnorlaw(mea_th, sqrt(var_th/n), t),%), \+ 100]:\npar_meab:= [seq(%[k]..%[k+1], k=1..cut)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 992 "par_meab := [0 .. 5.5166243918549038065, 5.5 166243918549038065 .. 5.6152038088672296221, 5.6152038088672296221 .. \+ 5.6817453405764927220, 5.6817453405764927220 .. 5.7389672736121728588, 5.7389672736121728588 .. 5.7910205385468090103, 5.7910205385468090103 .. 5.8367914261165388899, 5.8367914261165388899 .. 5.8739485804176314 250, 5.8739485804176314250 .. 5.9140587650763738895, 5.914058765076373 8895 .. 5.9485877024651133602, 5.9485877024651133602 .. 5.982210103173 4702731, 5.9822101031734702731 .. 6.0155981523222433701, 6.01559815232 22433701 .. 6.0473515068172300584, 6.0473515068172300584 .. 6.08271737 54123441353, 6.0827173754123441353 .. 6.1168837368573205088, 6.1168837 368573205088 .. 6.1551948341234968150, 6.1551948341234968150 .. 6.1947 812825296183732, 6.1947812825296183732 .. 6.2372604473898537161, 6.237 2604473898537161 .. 6.2943935621882849493, 6.2943935621882849493 .. 6. 3652490970730497454, 6.3652490970730497454 .. 6.4730517797290572688, 6 .4730517797290572688 .. 100.]:nops(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 190 "[seq(5.+rand()/divi, k=1..cut2)]: %/add(k,k=%):\n[se q(add(%[j],j=1..k),k=1..cut2-1)]:\n[0, (op@map)(t->ICnorlaw(mea_th, sq rt(var_th/n), t),%), 100]:\npar_meab2:= [seq(%[k]..%[k+1], k=1..cut2)] :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 754 "par_meab2 := [0 .. 5. 5708727145801166212, 5.5708727145801166212 .. 5.6822464209763361016, 5 .6822464209763361016 .. 5.7546695388155269593, 5.7546695388155269593 . . 5.8159854796639388584, 5.8159854796639388584 .. 5.864774591335891738 2, 5.8647745913358917382 .. 5.9097684791009546936, 5.90976847910095469 36 .. 5.9586932690133206101, 5.9586932690133206101 .. 6.00092380493693 31255, 6.0009238049369331255 .. 6.0431197492592126891, 6.0431197492592 126891 .. 6.0866327842520709031, 6.0866327842520709031 .. 6.1388212864 138194373, 6.1388212864138194373 .. 6.1903201386667816286, 6.190320138 6667816286 .. 6.2533207294320592545, 6.2533207294320592545 .. 6.328386 5299659590743, 6.3283865299659590743 .. 6.4415587225811864153, 6.44155 87225811864153 .. 100.]: nops(%);" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 23 "varb : equ(21), par(21)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 244 "formule_variance_predicteur_s2;\nvar_sig2:= mu4_th/n-(n-3)/n/(n -1)*var_th^2: var_th, var_sig2;\nlaw_varb:= t->norlaw(var_th, sqrt(var _sig2), t); \nLaw_varb:= t->Cnorlaw(var_th, sqrt(var_sig2), t): \npv0 := plot(law_varb(t), t=7..13, linestyle=24): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 136 "fac:=4: ran:= 16/2..51/4: floor(op(1,%)*fac)..f loor(op(2,%)*fac-1):\nequ_varb:= [0..16/2,seq(k/fac..(k+1)/fac,k=%), 5 1/4..100]; nops(%);\n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 186 "[ seq(5.+rand()/divi, k=1..cut)]: %/add(k,k=%):\n[seq(add(%[j],j=1..k),k =1..cut-1)]:\n[0, (op@map)(t->ICnorlaw(var_th, sqrt(var_sig2), t),%), \+ 100]:\npar_varb:= [seq(%[k]..%[k+1], k=1..cut)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 993 "par_varb := [0 .. 8.4825160437807244999, 8.4 825160437807244999 .. 8.7714993253539456223, 8.7714993253539456223 .. \+ 8.9552387516947884581, 8.9552387516947884581 .. 9.1047774596540501023, 9.1047774596540501023 .. 9.2511641918682500361, 9.2511641918682500361 .. 9.3637332320063885654, 9.3637332320063885654 .. 9.4794961667159399 508, 9.4794961667159399508 .. 9.5804639677977904208, 9.580463967797790 4208 .. 9.6724084869566296642, 9.6724084869566296642 .. 9.773839132786 1848179, 9.7738391327861848179 .. 9.8675033383746591840, 9.86750333837 46591840 .. 9.9725047356575813922, 9.9725047356575813922 .. 10.0779790 52520288295, 10.077979052520288295 .. 10.190200043406175900, 10.190200 043406175900 .. 10.307708873412809400, 10.307708873412809400 .. 10.426 901903780647982, 10.426901903780647982 .. 10.563996809166069392, 10.56 3996809166069392 .. 10.713770058728527869, 10.713770058728527869 .. 10 .915222885499237957, 10.915222885499237957 .. 11.186045407708227399, 1 1.186045407708227399 .. 100.]: nops(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 23 "chib : equ( 21), par(21)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "law_chib:= \+ t->chi2(n6-1, t); \nLaw_chib:= t->Chi2(n6-1, t):\npc0:= plot(law_chib( t), t= 0..35, linestyle=24): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 131 "fac:=2/3: ran:= 0..30; floor(op(1,%)*fac)..floor(op(2,%)*fac- 1);\nequ_chib:= evalf([seq(k/fac..(k+1)/fac,k=%),30..100],3); nops(%); \n" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 166 "[seq(5.+rand()/divi, k=1..cut)]: %/add(k,k=%):\n[seq(add(%[j],j=1..k),k=1..cut-1)]:\n [0, \+ (op@map)(t->IChi(n6-1, t),%), 100.]:\npar_chib:= [seq(%[k]..%[k+1], k= 1..cut)]:" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 992 "par_chib := [0 .. 3.8385888104245271518, 3.8385888104245271518 .. 4.7428297843206400955, 4.7428297843206400955 .. 5.4504676610764523829 , 5.4504676610764523829 .. 6.0304066943584594707, 6.030406694358459470 7 .. 6.5691594657234704425, 6.5691594657234704425 .. 7.094899404535529 3077, 7.0948994045355293077 .. 7.6259325952322011777, 7.62593259523220 11777 .. 8.1009562715697566513, 8.1009562715697566513 .. 8.59537193734 82310549, 8.5953719373482310549 .. 9.1136159666007951112, 9.1136159666 007951112 .. 9.6015586414332681239, 9.6015586414332681239 .. 10.186465 962899603680, 10.186465962899603680 .. 10.752018554488099405, 10.75201 8554488099405 .. 11.324145733125129257, 11.324145733125129257 .. 11.97 4170813091047527, 11.974170813091047527 .. 12.690947688749220339, 12.6 90947688749220339 .. 13.517540949908630426, 13.517540949908630426 .. 1 4.588046197538691878, 14.588046197538691878 .. 15.994599971988317277, \+ 15.994599971988317277 .. 18.489802623737718391, 18.489802623737718391 \+ .. 100.]:nops(%);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "ASSE RT(type(par_meab, [range$cut])),ASSERT(type(par_varb, [range$cut])),AS SERT(type(par_chib, [range$cut])); map(nops, [par_meab, par_varb, par_ chib]);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 37 "Traitements des jour s d'un mois donn\351" }}{EXCHG {PARA 0 "" 0 "" {TEXT -1 29 "On v\351ri fie qu'ils existent..." }}{PARA 0 "" 0 "" {MPLTEXT 0 21 128 "for qzq t o Q do \n try fopen( cat(ici, table_seed[qzq]), READ); fclose(%); \n c atch : print(qzq, table_seed[qzq]);\n end try; \nod;:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 28 "Traitement equidistant (equ)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "name_equ:= cat(ici,\".equ_test\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 142 "try read name_equ;\ncatch : equ_test:= t able(): Q:=0; save n6, n, M, Q, equ_test, name_equ; \nend try; deja_t raites=Q; ASSERT(Q<=Qx, `bad Qx`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 699 "stamp:= time(); for qzq from Q+1 to Qx do \nread cat (ici, table_seed[qzq]):\nconvert(m_mea,list): li_mea:= transform[tally ](%):\n tal_mea:= transform[tallyinto](li_mea, equ_meab):\n tmea:= tes t_law_chi(tal_mea, Law_meab, M);\nconvert(m_var,list): li_var:= trans form[tally](%):\n tal_var:= transform[tallyinto](li_var, equ_varb):\n \+ tvar:= test_law_chi( tal_var, Law_varb, M);\nconvert(m_chi,list): li_ chi:= transform[tally](%):\n tal_chi:= transform[tallyinto](li_chi, eq u_chib):\n tchi:=test_law_chi( tal_chi, Law_chib, M);\nequ_test[table _seed[qzq]]:= tmea,tvar,tchi;\nod: Q:= Qx:\nsave n6,n,M,Q, equ_test, n ame_equ;\nlaps:= time()- stamp; \n# duree = 944.709 \n# laps = 5573.98 1 (rat\351s dans evalf = plus long) " }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 29 "Traitement equiprobable (par)" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 32 "name_par:= cat(ici,\".par_test\");" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "try read name_par;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 123 "catch : par_test:= table(): Q:=0; save n6, n, \+ M, Q, par_test, name_par; \nend try; deja_traites=Q; ASSERT(Q<=Qx, `ba d Qx`);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "# Q:=0; " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 743 "stamp:= time(); for qzq fro m Q+1 to Qx do \nread cat(ici, table_seed[qzq]):\nconvert(m_mea,list): li_mea:= transform[tally](%):\n tal_mea:= transform[tallyinto](li_mea , par_meab):\n tmea:= test_law_chi(tal_mea, Law_meab, M);\nconvert(m_ var,list): li_var:= transform[tally](%):\n tal_var:= transform[tallyin to](li_var, par_varb):\n tvar:= test_law_chi( tal_var, Law_varb, M); \nconvert(m_chi,list): li_chi:= transform[tally](%):\n tal_chi:= trans form[tallyinto](li_chi, par_chib):\n tchi:=test_law_chi( tal_chi, Law_ chib, M);\npar_test[table_seed[qzq]]:= tmea,tvar,tchi;\n# print(qzq,% );\nod: Q:= Qx;\nsave n6,n,M,Q, par_test, name_par;\nlaps:= time()- st amp;\n# laps = 884.060\n# laps = 6475.354 (Q=1657)\n# laps = 6033.347 \+ (Q=1657)\n# laps = 5944.596 (Q=1657)" }}}}{EXCHG {PARA 0 "" 0 "" {MPLTEXT 0 21 333 "par_test3:= table(): for qzq in table_seed do \nrea d cat(ici, qzq):\nconvert(m_mea,list): li_mea:= transform[tally](%):\n tal_mea:= transform[tallyinto](li_mea, par_meab2):\n tmea:= test_law_ chi(tal_mea, Law_meab, M);\npar_test3[qzq]:= tmea;\n if (max)(%)>34 t hen print (qzq, %) fi;\nod:\ncat(ici,\".par_test3\"); save n6,n,M,Q, p ar_test3, %;" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 56 "Graphes associ\351s \340 un jour donn \351 (M batches de taille n)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "read cat(ici, table_seed[22]):" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 5 "mean " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "convert(m_me a,list): li_mea:= transform[tally](%):\n'esp(m_mea)'=mean(li_mea), 'va r(m_mea)'=variance(li_mea);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 135 "tal_mea_cut:= cut_n(li_mea, cut): pzz:= histo(%, area=1):\nday[1] := displayg(pm0,pzz): day_red[1]:= test_law(tal_mea_cut, Law_meab, M) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "tal_mea_par:= transfo rm[tallyinto](li_mea, par_meab): pzz:= histo(%, area=1):\nday[2]:= dis playg(pm0,pzz): day_red[2]:= test_law(tal_mea_par, Law_meab, M):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 156 "tal_mea_equ:= transform[tal lyinto](li_mea, equ_meab): pzz:= histo(%, area=1): \nday[3]:= displayg (pm0,pzz): day_red[3]:= test_law(tal_mea_equ, Law_meab, M):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 385 "xla:= 2.5: tick1:= 5: tick2 := 7: \ndisplay(day[1], plottools[transform]((x,y)->[x+xla,y])(day[2]) ,\nplottools[transform]((x,y)->[x+2*xla,y])(day[3]), view=[5..12.5, DE FAULT],\nxtickmarks=[seq(tick1+xla*k=tick1,k=0..2), seq(tick2+xla*k=ti ck2,k=0..2)],\nytickmarks=[1.4]);\n(chi^2)[reduced]=seq(day_red[k],k=1 ..3);\n'esp(m_mea)'= evalf(mean(li_mea),5), 'var(m_mea)'= evalf(varian ce(li_mea),5);" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 9 "variance " }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "convert(m_var,list): li_var: = transform[tally](%):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 " tal_var_cut:= cut_n(li_var, cut): pzz:= histo(%, area=1 ):\nday[3+1]:= displayg(pv0,pzz): day_red[3+1]:= test_law(tal_var_cut, Law_varb, M):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "tal_var _par:= transform[tallyinto](li_var, par_varb): pzz:= histo(%, area=1): \nday[3+2]:= displayg(pv0,pzz): day_red[3+2]:= test_law(tal_var_par, L aw_varb, M):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 160 "tal_var_e qu:= transform[tallyinto](li_var, equ_varb): pzz:= histo(%, area=1): \+ \nday[3+3]:= displayg(pv0,pzz): day_red[3+3]:= test_law(tal_var_equ, L aw_varb, M):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 391 "xla:= 7: \+ tick1:= 8: tick2:= 12: \ndisplay(day[3+1], plottools[transform]((x,y)- >[x+xla,y])(day[3+2]),\nplottools[transform]((x,y)->[x+2*xla,y])(day[3 +3]), \nview=[7..27, DEFAULT],\nxtickmarks=[seq(tick1+xla*k=tick1,k=0. .2), seq(tick2+xla*k=tick2,k=0..2)],\nytickmarks=[0.5]);\n(chi^2)[redu ced]=seq(day_red[3+k],k=1..3);\n'esp(m_var)'= evalf(mean(li_var),5), ' var(m_var)'= evalf(variance(li_var),5);" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 9 "chisquare" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "con vert(m_chi,list): li_chi:= transform[tally](%):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 154 "tal_chi_cut:= cut_n(li_chi, cu t): pzz:= histo(%, area=1):\nday[6+1]:= displayg(pc0,pzz): day_red[6+1 ]:= test_law(tal_chi_cut, Law_chib, M):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 159 "tal_chi_par:= transform[tallyinto](li_chi, par_chib) : pzz:= histo(%, area=1):\nday[6+2]:= displayg(pc0,pzz): day_red[6+2]: = test_law(tal_chi_par, Law_chib, M):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 160 "tal_chi_equ:= transform[tallyinto](li_chi, equ_chib) : pzz:= histo(%, area=1): \nday[6+3]:= displayg(pc0,pzz): day_red[6+3] := test_law(tal_chi_equ, Law_chib, M):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 392 "xla:= 30: tick1:= 8: tick2:= 30: \ndisplay(day[6+1], plottools[transform]((x,y)->[x+xla,y])(day[6+2]),\nplottools[transfor m]((x,y)->[x+2*xla,y])(day[6+3]), \nview=[0..90, DEFAULT],\nxtickmarks =[seq(tick1+xla*k=tick1,k=0..2), seq(tick2+xla*k=tick2,k=0..2)],\nytic kmarks=[0.1]);\n(chi^2)[reduced]=seq(day_red[6+k],k=1..3);\n'esp(m_chi )'= evalf(mean(li_chi),5), 'var(m_chi)'= evalf(variance(li_chi),5);" } }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "bilan_des_day_red := matr ix(3,3,[seq(day_red[k],k=1..9)]);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 48 "Test (equ) * *equi-distant** d'un mois de Q jours" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "alias(test= equ_test); dis:='dis':" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Le mod\350le est le m\352me pour tous les chi_x xx" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "law_cz:= t->chi2(cut-1,t): L aw_cz:= t->Chi2(cut-1,t):\nILawcz:= t->IChi(cut-1,t): \nqz:= plot(law_ cz(t), t=0..50, linestyle=24): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "cut_cut:=17: \n[0,seq(ILawcz(k/cut_cut), k=1..cut_cut-1),105. ]:\ndecoupe_par:= [seq(%[k]..%[k+1], k=1..cut_cut)]: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "ILawcz(0.5/cut_cut): ILawcz(1-0.5/ cut_cut): \n[0, seq((%*k+(cut_cut-2-k)*%%)/(cut_cut-2), k=0.. cut_cut- 2), 105.]: \ndecoupe_try:= [seq(%[k]..%[k+1],k=1..cut_cut)]: " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 16 "Etude de chi_mea" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "chi_mea:= transform[tally]([seq(test[table_seed[q]][1],q=1..Q)]) :" }{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Cut equi-effe ctif, equi-probable, equi-distant(*)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "chi_mea_cut:= cut_n(chi_mea, cut_cut): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 97 "qzz:= histo(%,area=1):\nchi_red[1]:= test_law(chi_mea _cut, Law_cz, Q): dis[1]:= displayg(qz,qzz): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "chi_mea_par:= transform[tallyinto](chi_mea, decoupe_ par):qzz:= histo(%,area=1):\nchi_red[2]:= test_law(chi_mea_par, Law_cz , Q): dis[2]:= displayg(qz,qzz): " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "chi_mea_try:= transform[tallyinto](chi_mea, decoupe_try):qzz:= hi sto(%,area=1):\nchi_red[3]:= test_law(chi_mea_try, Law_cz, Q): dis[3]: = displayg(qz,qzz):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "xla:= 60:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 367 "display(dis[1], plo ttools[transform]((x,y)->[x+xla,y])(dis[2]),\nplottools[transform]((x, y)->[x+2*xla,y])(dis[3]), \nview=[0..170, DEFAULT],\nxtickmarks=[seq(c ut-1+xla*k=cut-1,k=0..2),\n seq(2*(cut-1)+xla*k=2*(cut-1),k=0..2)],yti ckmarks=[0.07]);\n(chi^2)[reduced]=seq(chi_red[k],k=1..3);\n'mean(chi_ mea)'= evalf(mean(chi_mea),5), 'var(chi_mea)'= evalf(variance(chi_mea) ,5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 16 " Etude de chi_var" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "chi_var: = transform[tally]([seq(test[table_seed[q]][2],q=1..Q)]):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Cut equi-effectif, equi-probable, equi-di stant(*)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 140 "chi_var_cut:= cut_n(ch i_var, cut_cut): qzz:= histo(%,area=1):\nchi_red[3+1]:= test_law(chi_v ar_cut, Law_cz, Q): dis[3+1]:= displayg(qz,qzz): " }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 158 "chi_var_par:= transform[tallyinto](chi_var, decoupe_par):qzz:= histo(%,area=1):\nchi_red[3+2]:= test_law(chi_var_ par, Law_cz, Q): dis[3+2]:= displayg(qz,qzz): " }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 157 "chi_var_try:= transform[tallyinto](chi_var, d ecoupe_try):qzz:= histo(%,area=1):\nchi_red[3+3]:= test_law(chi_var_tr y, Law_cz, Q): dis[3+3]:= displayg(qz,qzz):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "xla:=60:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 377 "display(dis[3+1], plottools[transform]((x,y)->[x+xla,y])(dis[3+2] ),\nplottools[transform]((x,y)->[x+2*xla,y])(dis[3+3]), \nview=[0..170 , DEFAULT],\nxtickmarks=[seq(cut-1+xla*k=cut-1,k=0..2),\n seq(2*(cut-1 )+xla*k=2*(cut-1),k=0..2)],ytickmarks=[0.07]);\n(chi^2)[reduced]=seq(c hi_red[k],k=3+1..3+3);\n'mean(chi_var)'= evalf(mean(chi_var),5), 'var( chi_var)'= evalf(variance(chi_var),5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 16 "Etude de ch i_chi" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "chi_chi:= transform [tally]([seq(test[table_seed[q]][3],q=1..Q)]):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Cut equi-effectif, equi-probable, equi-distant(*)" } }{PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "chi_chi_cut:= cut_ n(chi_chi, cut_cut):qzz:= histo(%,area=1):\nchi_red[6+1]:= test_la w(chi_chi_cut, Law_cz, Q): dis[6+1]:= displayg(qz,qzz): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "chi_chi_par:= transform[tallyinto] (chi_chi, decoupe_par):qzz:= histo(%,area=1):\nchi_red[6+2]:= test_law (chi_chi_par, Law_cz, Q): dis[6+2]:= displayg(qz,qzz): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 157 "chi_chi_try:= transform[tallyinto] (chi_chi, decoupe_try):qzz:= histo(%,area=1):\nchi_red[6+3]:= test_law (chi_chi_try, Law_cz, Q): dis[6+3]:= displayg(qz,qzz):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "xla:=60:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 377 "display(dis[6+1], plottools[transform]((x,y)->[x+x la,y])(dis[6+2]),\nplottools[transform]((x,y)->[x+2*xla,y])(dis[6+3]), \nview=[0..170, DEFAULT],\nxtickmarks=[seq(cut-1+xla*k=cut-1,k=0..2), \n seq(2*(cut-1)+xla*k=2*(cut-1),k=0..2)],ytickmarks=[0.07]);\n(chi^2) [reduced]=seq(chi_red[k],k=6+1..6+3);\n'mean(chi_chi)'= evalf(mean(chi _chi),5), 'var(chi_chi)'= evalf(variance(chi_chi),5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "bilan_des_chi_red_equ := matrix(3,3,[seq(chi_red[k],k =1..9)]);" }{TEXT -1 0 "" }{MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 49 "Test (p ar) **equi-probable** d'un mois de Q jours" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 34 "alias(test= par_test); dis:='dis':" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 43 "Le mod\350le est le m\352me pour tous les chi_xxx" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "law_cz:= t->chi2(cut-1 ,t): Law_cz:= t->Chi2(cut-1,t):\nILawcz:= t->IChi(cut-1,t): \nqz:= plo t(law_cz(t), t=0..50, linestyle=24): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 112 "cut_cut:=17: \n[0,seq(ILawcz(k/cut_cut), k=1..cut_cu t-1),100.]:\ndecoupe_par:= [seq(%[k]..%[k+1], k=1..cut_cut)]: " }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 163 "ILawcz(0.5/cut_cut): ILawcz (1-0.5/cut_cut): \n[0, seq((%*k+(cut_cut-2-k)*%%)/(cut_cut-2), k=0.. c ut_cut-2), 100.]: \ndecoupe_try:= [seq(%[k]..%[k+1],k=1..cut_cut)]: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 16 "Etude de chi_mea" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "chi_mea:= transform[tally]([seq(test[table_seed[q]][1],q=1..Q) ]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "cut:= 21; qz:= plot( law_cz(t), t=0..50, linestyle=24):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Cut equi-effectif, equi-probable, equi-distant(*)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 136 "chi_mea_cut:= cut_n(chi_mea, cut_cut): qzz:= histo(%,area=1):\nchi_red[1]:= test_law(chi_mea_cut, Law_cz, Q): dis[ 1]:= displayg(qz,qzz): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "chi_mea_par:= transform[tallyinto](chi_mea, decoupe_par):qzz:= histo( %,area=1):\nchi_red[2]:= test_law(chi_mea_par, Law_cz, Q): dis[2]:= di splayg(qz,qzz): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 153 "chi_me a_try:= transform[tallyinto](chi_mea, decoupe_try):qzz:= histo(%,area= 1):\nchi_red[3]:= test_law(chi_mea_try, Law_cz, Q): dis[3]:= displayg( qz,qzz):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "xla:=60:" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 367 "display(dis[1], plottools[transform]((x,y)->[x+xla ,y])(dis[2]),\nplottools[transform]((x,y)->[x+2*xla,y])(dis[3]), \nvie w=[0..170, DEFAULT],\nxtickmarks=[seq(cut-1+xla*k=cut-1,k=0..2),\n seq (2*(cut-1)+xla*k=2*(cut-1),k=0..2)],ytickmarks=[0.07]);\n(chi^2)[reduc ed]=seq(chi_red[k],k=1..3);\n'mean(chi_mea)'= evalf(mean(chi_mea),5), \+ 'var(chi_mea)'= evalf(variance(chi_mea),5);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{SECT 0 {PARA 4 "" 0 "" {TEXT -1 16 "Etude de chi_var" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "chi_var:= transform[tally]([seq(tes t[table_seed[q]][2],q=1..Q)]):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Cut equi-effectif, equi-probable, equi-distant(*)" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 140 "chi_var_cut:= cut_n(chi_var, cut_cut): qzz:= histo (%,area=1):\nchi_red[3+1]:= test_law(chi_var_cut, Law_cz, Q): dis[3+1] := displayg(qz,qzz): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "c hi_var_par:= transform[tallyinto](chi_var, decoupe_par):qzz:= histo(%, area=1):\nchi_red[3+2]:= test_law(chi_var_par, Law_cz, Q): dis[3+2]:= \+ displayg(qz,qzz): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 157 "chi_ var_try:= transform[tallyinto](chi_var, decoupe_try):qzz:= histo(%,are a=1):\nchi_red[3+3]:= test_law(chi_var_try, Law_cz, Q): dis[3+3]:= dis playg(qz,qzz):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "xla:=60:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 377 "display(dis[3+1], plottools[transform]((x,y )->[x+xla,y])(dis[3+2]),\nplottools[transform]((x,y)->[x+2*xla,y])(dis [3+3]), \nview=[0..170, DEFAULT],\nxtickmarks=[seq(cut-1+xla*k=cut-1,k =0..2),\n seq(2*(cut-1)+xla*k=2*(cut-1),k=0..2)],ytickmarks=[0.07]);\n (chi^2)[reduced]=seq(chi_red[k],k=3+1..3+3);\n'mean(chi_var)'= evalf(m ean(chi_var),5), 'var(chi_var)'= evalf(variance(chi_var),5);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{SECT 0 {PARA 4 "" 0 " " {TEXT -1 16 "Etude de chi_chi" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "chi_chi:= transform[tally]([seq(test[table_seed[q]][3],q=1..Q) ]):" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 49 "Cut equi-effectif, equi-pr obable, equi-distant(*)" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "chi_chi_ cut:= cut_n(chi_chi, cut_cut): qzz:= histo(%,area=1 ):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "chi_red[6+1]:= test_law(chi_c hi_cut, Law_cz, Q): dis[6+1]:= displayg(qz,qzz): " }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 158 "chi_chi_par:= transform[tallyinto](chi_chi, decoup e_par):qzz:= histo(%,area=1):\nchi_red[6+2]:= test_law(chi_chi_par, La w_cz, Q): dis[6+2]:= displayg(qz,qzz): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 157 "chi_chi_try:= transform[tallyinto](chi_chi, decoupe_ try):qzz:= histo(%,area=1):\nchi_red[6+3]:= test_law(chi_chi_try, Law_ cz, Q): dis[6+3]:= displayg(qz,qzz):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "xla:=60: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 377 "display(dis[6+1], plot tools[transform]((x,y)->[x+xla,y])(dis[6+2]),\nplottools[transform]((x ,y)->[x+2*xla,y])(dis[6+3]), \nview=[0..170, DEFAULT],\nxtickmarks=[se q(cut-1+xla*k=cut-1,k=0..2),\n seq(2*(cut-1)+xla*k=2*(cut-1),k=0..2)], ytickmarks=[0.07]);\n(chi^2)[reduced]=seq(chi_red[k],k=6+1..6+3);\n'me an(chi_chi)'= evalf(mean(chi_chi),5), 'var(chi_chi)'= evalf(variance(c hi_chi),5);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "bilan_des_c hi_red_par := matrix(3,3,[seq(chi_red[k],k=1..9)]);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "evalm(bilan_des_day_red);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "evalm(bilan_des_chi_red_equ); lprint(); evalm(bilan_des_chi_re d_par);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "tmp:= map(conver t, li_chi, list): convert(map2(op,2,tmp),set);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "map2(op,1,tmp): pl:= plots[pointplot]([seq([k,0],k=%) ]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "display(pl, view=[5..30,DEFA ULT], axes=none);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "tmp:= \+ map(convert, li_mea, list): convert(map2(op,2,tmp),set);" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "map2(op,1,tmp): pl:= plots[pointplot]([seq([k ,0],k=%)]):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "display(pl, view=[5. 5 .. 6.5,DEFAULT], axes=none);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "53" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 1 1 1 33 1 1 }