{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 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 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 "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 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 "Norma l" -1 258 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 }{PSTYLE "Title" -1 259 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 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "restart: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "with(pldx): with(plots, display, po intplot):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "with(stats): w ith(describe): with(statplots):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "with(plottools): with(student):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "with(simul);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 283 "printma:= proc(ma_) local ma,j,k,jx,kx: \nif printmaspec <> tru e then return print(ma_) fi; \nma:= convert(ma_, matrix): jx,kx:= row dim(ma), coldim(ma); print(%);\nfor j to jx do for k to kx do print(ma [j,k]); od;od; \nprint(\"*********** fin **************\");\nend: pri ntmaspec:= false;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "" 0 "" {TEXT -1 22 "Formule de la variance" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 50 "add((x[j]-a)^2, j=1..4); xcs(%,a,x[1],x[2], x[3]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 10 "Un exemple" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "li:= [1,9,37,59,40,11,3];" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 60 "dist:= [seq(Weight((k-1)*3.5..k*3.5,li[k]), k=1..no ps(li))]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 ";" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "displayf(histogram(dist), \+ tickmarks=[3,3]); [count,mean,median,mode](dist);" }{TEXT -1 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 66 "map2(op,1,dist): ran:=((min. .max)@op@map)(op,%); nn:= count(dist);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "[lhs(ran),0]: for k to nops(li) do %,[op([1,2], dist [k]), %[-1][2]+ op(2,dist[k]) ]; od: cumul_croit:= %; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "[rhs(ran),0]: for k from nops(li) \+ to 1 by -1 do %,[op([1,1], dist[k]), %[-1][2]+ op(2,dist[k]) ]; od: cu mul_decroit:= %; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 278 "pl1:= plot([cumul_croit], linestyle=24, color= black):\npl2:= plot([cumul_d ecroit], linestyle=24, color= black):\npl3:= seq(plot([x,nn/4*k,x=0..r hs(ran)]), k=1..3):\nqua:= seq(quartile[k](dist), k=1..3),rhs(ran);\np l4:= seq(plot([quartile[k](dist),y,y=0..nn], numpoints=2), k=1..3):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "displayf(pl1,pl2,pl3,pl4, \+ tickmarks=[evalf([qua],3),[0,40,80,120,160]]);" }}}}{SECT 0 {PARA 3 " " 0 "" {TEXT -1 16 "Un autre exemple" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 200 "exo:= 1948, 1946, 1946, 1945, 1953, 1953, 1951, 1950 ,\n1950, 1956, 1957, 1949, 1940, 1949, 1948, 1960, \n1944, 1953, 1941, 1956, 1942, 1956, 1963, 1954, \n1958, 1945, 1949, 1955, 1962, 1957, 1 946, 1951; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "sexo:= sort( [exo]); dist:= xtally(%): dist0:= %:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "interface(rtablesize=20): ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "displayf(histogram(dist), tickmarks=[3,3]); " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "ran:=sexo[1]..sexo[-1]+1; nn:= count(dist); mu0:= mean(dist)*1.; var0:= variance(dist)*1.;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "nops(dist); op([2], dist[1]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 103 "[lhs(ran),0]; for k to nops(dist) do %,[op(1, dist[k ]), %[-1][2]+ op(2,dist[k]) ]; od: cumul_croit:= %:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 121 "[rhs(ran),0]: for k from nops(dist) to 1 by -1 do %,[op([1], dist[k]), %[-1][2]+ op(2,dist[k]) ]; od: cumul_decroit:= % :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 281 "pl1:= plot([cumul_cr oit], linestyle=24, color= black):\npl2:= plot([cumul_decroit], linest yle=24, color= black):\npl3:= seq(plot([x,nn/4*k,x=(ran)]), k=1..3):\n qua:= lhs(ran),seq(quartile[k](dist), k=1..3),rhs(ran):\npl4:= seq(plo t([quartile[k](dist),y,y=0..nn], numpoints=2), k=1..3):" }{TEXT -1 0 " " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "displayf(pl1,pl2,pl3,pl4, tickm arks=[evalf([qua],5),[nn/2,nn]]);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "Regroupements" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 158 "nx: =6: deb:= lhs(ran): delta:= (rhs(ran)-lhs(ran))/nx: [seq(deb+k*delta.. deb+(k+1)*delta,k=0..nx-1)]:\ndist:= stats[transform, tallyinto](dist0 , %): dist1:=% :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 ";" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "displayf(histogram( dist), tickmarks=[3,3]); " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "mu1:= mean(dist)*1.; var1:= varianc e(dist)*1.;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 108 "[lhs(ran),0 ]: for k to nops(dist) do %,[op([1,2], dist[k]), %[-1][2]+ op(2,dist[k ]) ]; od: cumul_croit:= % ;" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 125 "[rh s(ran)+1,0]: for k from nops(dist) to 1 by -1 do %,[op([1,1], dist[k]) , %[-1][2]+ op(2,dist[k]) ]; od: cumul_decroit:= % ;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 349 "pl1:= plot([cumul_croit], linestyle=24, \+ color= black):\npl2:= plot([cumul_decroit], linestyle=24, color= black ):\npl3:= seq(plot([x,nn/4*k,x=(ran)]), k=1..3):\nqua:= lhs(ran),seq(q uartile[k](dist), k=1..3),rhs(ran)+1:\npl4:= seq(plot([quartile[k](dis t),y,y=0..nn], numpoints=2), k=1..3): \ndisplayf(pl1,pl2,pl3,pl4, tick marks=[evalf([qua],5),[nn/2,nn]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "mu0; mu0-mu1; var0, var1, var0-var1;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 17 "Corr\351lati ons (DO)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "ran:= proc() ran d()/999999999989. end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "l ix:= [ '2+5*ran()'$10];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 " lip:= [seq(evalf([k, 2*k+5*ran()],3), k=lix)];" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 85 "ranx:= ((min-1..max+1)@op@map2)(op,1,lip); ran y:= ((min-1..max+1)@op@map2)(op,2,lip);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "sums:= s0= add(1,k=lip), s1= add(k[1],k=lip), s2= ad d(k[2],k=lip),\ns3= add(k[1]^2,k=lip), s4= add(k[1]*k[2],k=lip), s5= a dd(k[2]^2,k=lip);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "rels:= n=s0, mx*n=s1, my*n=s2, (varx+mx^2)*n=s3, (cov+mx*my)*n=s4, (vary+my^ 2)*n=s5; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "subs(sums, \{r els\}); prm:= solve(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 " subs(prm, [[mx-sqrt(varx),mx+sqrt(varx)], \n[my-sqrt(vary),my+sqrt(var y)]]): tick:= evalf(%,3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "frv:=subs(prm, 1/(1-cov^2/varx/vary)); sdr:= sqrt(subs(prm, vary/% ));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "subs(prm, my+cov/va rx*(x-mx)); \npl3:= plot(%,x=ranx, linestyle=24), \nplot(%+sdr,x=ranx, color=black), plot(%-sdr,x=ranx, color=black):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 141 "pl2:= plot(subs(prm, \{[mx-sqrt(varx),y,y=ran y], [mx+sqrt(varx),y,y=rany], \n[x,my-sqrt(vary),x=ranx],[x,my+sqrt(va ry),x=ranx]\}), color=black):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "pl1:= pointplot(lip, color=black):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "display(pl1, pl2, pl3, tickmarks=tick, view=[ranx, ra ny]);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 17 "Corr\351lations (DO)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "lix:= [ '2+5*ran()'$10];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 47 "lip:= [seq(evalf([k, -2*k +7*ran()],3), k=lix)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "r anx:= ((min-1..max+1)@op@map2)(op,1,lip); rany:= ((min-1..max+1)@op@ma p2)(op,2,lip);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "sums:= s 0= add(1,k=lip), s1= add(k[1],k=lip), s2= add(k[2],k=lip),\ns3= add(k[ 1]^2,k=lip), s4= add(k[1]*k[2],k=lip), s5= add(k[2]^2,k=lip);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "rels:= n=s0, mx*n=s1, my*n=s 2, (varx+mx^2)*n=s3, (cov+mx*my)*n=s4, (vary+my^2)*n=s5; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "subs(sums, \{rels\}); prm:= solve(% );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 "subs(prm, [[mx-sqrt(v arx),mx+sqrt(varx)], \n[my-sqrt(vary),my+sqrt(vary)]]): tick:= evalf(% ,3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "frv:=subs(prm, 1/(1 -cov^2/varx/vary)); sdr:= sqrt(subs(prm, vary/%));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "subs(prm, my+cov/varx*(x-mx)); \npl3:= plo t(%,x=ranx, linestyle=24), \nplot(%+sdr,x=ranx, color=black), plot(%-s dr,x=ranx, color=black):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "pl2:= plot(subs(prm, \{[mx-sqrt(varx),y,y=rany], [mx+sqrt(varx),y ,y=rany], \n[x,my-sqrt(vary),x=ranx],[x,my+sqrt(vary),x=ranx]\}), colo r=black):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "pl1:= pointplo t(lip, color=black):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 "dis play(pl1, pl2, pl3, tickmarks=tick, view=[ranx, rany], axes= framed); " }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 17 "Corr\351lations (DO)" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "ran:= proc() rand()/99999999 9989. end;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "lix:= [ '1+4* ran()'$10];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "lip:= [seq(e valf([k, 2*k+ran()],3), k=lix)];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "ranx:= ((min-1..max+1)@op@map2)(op,1,lip); rany:= ((m in-1..max+1)@op@map2)(op,2,lip);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 138 "sums:= s0= add(1,k=lip), s1= add(k[1],k=lip), s2= ad d(k[2],k=lip),\ns3= add(k[1]^2,k=lip), s4= add(k[1]*k[2],k=lip), s5= a dd(k[2]^2,k=lip);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "rels:= n=s0, mx*n=s1, my*n=s2, (varx+mx^2)*n=s3, (cov+mx*my)*n=s4, (vary+my^ 2)*n=s5; " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "subs(sums, \{r els\}); prm:= solve(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 94 " subs(prm, [[mx-sqrt(varx),mx+sqrt(varx)], \n[my-sqrt(vary),my+sqrt(var y)]]): tick:= evalf(%,3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 69 "frv:=subs(prm, 1/(1-cov^2/varx/vary)); sdr:= sqrt(subs(prm, vary/% ));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 134 "subs(prm, my+cov/va rx*(x-mx)); \npl3:= plot(%,x=ranx, linestyle=24), \nplot(%+sdr,x=ranx, color=black), plot(%-sdr,x=ranx, color=black):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 68 "unapply(.708743350+1.901124791*x-y,x,y);\nadd( k^2, k=map(%@op, lip));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 141 "pl2:= plot(subs(prm, \{[mx-sqrt(varx),y,y=rany], [mx+sqrt(varx),y,y=r any], \n[x,my-sqrt(vary),x=ranx],[x,my+sqrt(vary),x=ranx]\}), color=bl ack):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "pl1:= pointplot(li p, color=black):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "display (pl1, pl2, pl3, tickmarks=tick, view=[ranx, rany]);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 18 " Corr\351lation (DG-1)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "jx :=3; kx:=3; Matrix(jx+5,kx+5, <<4|5|2>,<8|7|3>,<2|2|1>>, fill=``) : \n \n< <1,2,3,nk,yn,sxj,ysxj,y2 > | % > : " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 45 " dat:= <<`` |1|3|5|nj|xn|syk|xsyk|x2 >, %> : " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 717 "for j to jx do \n dat[j+1, kx+2]: = add(dat[j+1,k+1],k=1..kx); dat[j+1, kx+3]:=dat[j+1,1]*%; dat[j+1, kx +6]:=dat[j+1,1]*%; \n dat[j+1, kx+4]:= add(dat[j+1,k+1]*dat[1,k+1],k =1..kx); dat[j+1, kx+5]:=dat[j+1,1]*%; \nod : \nfor k to kx do \n dat [jx+2, k+1]:= add(dat[j+1,k+1],j=1..jx); dat[jx+3, k+1]:=dat[1,k+1]*%; dat[jx+6, k+1]:=dat[1,k+1]*%; \n dat[jx+4, k+1]:= add(dat[j+1,k+1]*d at[j+1,1],j=1..jx); dat[jx+5, k+1]:=dat[1,k+1]*%; \nod:\ndat[jx+2, kx+ 2]:= add(dat[j+1,kx+2],j=1..jx): \ndat[jx+2, kx+6]:= add(dat[j+1,kx+6] ,j=1..jx): dat[jx+6, kx+2]:= add(dat[jx+6,k+1],k=1..kx): \ndat[jx+4, k x+3]:= add(dat[j+1,kx+3],j=1..jx):\ndat[jx+3, kx+4]:= add(dat[jx+3,k+1 ],k=1..kx):\ndat[jx+5, kx+5]:= add(dat[jx+5,k+1],k=1..kx): \ndat;" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "ex:= dat[jx+4, kx+3]/dat[jx +2,kx+2]; ey:= dat[jx+3, kx+4]/dat[jx+2,kx+2];" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 111 "vx:= dat[jx+2, kx+6]/dat[jx+2,kx+2]-ex^2; vy: = dat[jx+6, kx+2]/dat[jx+2,kx+2]-ey^2; evalf([[ex,vx], [ey, vy]]);" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "vxy:= dat[jx+5, kx+5]/dat[j x+2,kx+2]-ex*ey;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "aa:= vx y/vx*1.; correl:= vxy/sqrt(vx*vy*1.);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 205 "rx:=0.3/2: ry:=0.6/2: with(plots, polygonplot):\npl1 := seq(seq(plot([dat[j+1,1]+rx*cos(t)*sqrt(dat[j+1,k+1]), dat[1,k+1]+r y*sin(t)*sqrt(dat[j+1,k+1]),t=0..2*Pi],\n numpoints=8, color=grey),k=1 ..kx),j=1..jx):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "pl2:= pl ot([ex+rx/2*cos(t), ey+ry/2*sin(t),t=0..2*Pi], color=black, numpoints= 8):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 106 "pl3:= plot([ex,y,y= 0..6], color=black, linestyle=24), plot([x,ey,x=0.5..3.5], color=blac k, linestyle=24):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "pl4:= \+ plot(aa*(x-ex)+ey,x=0.5..3.5,numpoints=3, color=black, linestyle=36): " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "displayf(pl3, pl4, subs (CURVES=POLYGONS,[pl2, pl1]), tickmarks=evalf([[ex],[ey]],3));" }}}} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 18 "Corr\351lation (DG-2)" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 58 "rrr:= rand(1..7): jx:=4; kx:=4; ma r:= matrix(jx,kx, rrr);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 72 " mar := matrix([[7, 3, 1, 1], [3, 7, 3, 1], [2, 2, 6, 3], [1, 3, 3, 4]] );" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "Matrix(jx+5,kx+5, con vert(mar, Matrix), fill=``): \n< <1,2,3,4,nk,yn,sxj,ysxj,y2 > | % > : \+ " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 47 " dat:= <<`` |1|2|3|4|nj|xn|syk| xsyk|x2 >, %> : " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 717 "for j \+ to jx do \n dat[j+1, kx+2]:= add(dat[j+1,k+1],k=1..kx); dat[j+1, kx+3 ]:=dat[j+1,1]*%; dat[j+1, kx+6]:=dat[j+1,1]*%; \n dat[j+1, kx+4]:= a dd(dat[j+1,k+1]*dat[1,k+1],k=1..kx); dat[j+1, kx+5]:=dat[j+1,1]*%; \no d : \nfor k to kx do \n dat[jx+2, k+1]:= add(dat[j+1,k+1],j=1..jx); d at[jx+3, k+1]:=dat[1,k+1]*%; dat[jx+6, k+1]:=dat[1,k+1]*%; \n dat[jx+ 4, k+1]:= add(dat[j+1,k+1]*dat[j+1,1],j=1..jx); dat[jx+5, k+1]:=dat[1, k+1]*%; \nod:\ndat[jx+2, kx+2]:= add(dat[j+1,kx+2],j=1..jx): \ndat[jx+ 2, kx+6]:= add(dat[j+1,kx+6],j=1..jx): dat[jx+6, kx+2]:= add(dat[jx+6, k+1],k=1..kx): \ndat[jx+4, kx+3]:= add(dat[j+1,kx+3],j=1..jx):\ndat[jx +3, kx+4]:= add(dat[jx+3,k+1],k=1..kx):\ndat[jx+5, kx+5]:= add(dat[jx+ 5,k+1],k=1..kx): \ndat;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "ex:= dat[jx+4, kx+3]/dat[jx+2,kx+2]; ey:= dat[jx+3, kx+4]/dat[jx+2,kx +2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "vx:= dat[jx+2, kx+ 6]/dat[jx+2,kx+2]-ex^2; vy:= dat[jx+6, kx+2]/dat[jx+2,kx+2]-ey^2; eval f([[ex,vx], [ey, vy]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 " vxy:= dat[jx+5, kx+5]/dat[jx+2,kx+2]-ex*ey;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 44 "aa:= vxy/vx*1.; correl:= vxy/sqrt(vx*vy*1.);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 205 "rx:=0.3/2: ry:=0.3/2: with( plots, polygonplot):\npl1:= seq(seq(plot([dat[j+1,1]+rx*cos(t)*sqrt(da t[j+1,k+1]), dat[1,k+1]+ry*sin(t)*sqrt(dat[j+1,k+1]),t=0..2*Pi],\n num points=8, color=grey),k=1..kx),j=1..jx):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "pl2:= plot([ex+rx/2*cos(t), ey+ry/2*sin(t),t=0..2*Pi] , \n color=black, numpoints=8):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 109 "pl3:= plot([ex,y,y=0..6], color=black, linestyle=24) , \n plot([x,ey,x=0..6], color=black, linestyle=24):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 71 "pl4:= plot(aa*(x-ex)+ey,x=0..6,nump oints=3, color=black, linestyle=36):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 78 "On a 44 point s avec x=1,2,3,4 et y=1,2,3,4\nsur une m\352me ligne, x est constant. " }}{PARA 0 "" 0 "" {TEXT -1 36 "sur une m\352me colonne, y est consta nt" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "printma(mar);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "printma(dat);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "'ex'=ex,'ey'=ey; 'vx'=vx, 'vxy'=vxy,'vy'=vy; \n'aa'=aa, 'correl'=correl, 'frv'=1/(1-correl^2);" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 125 "displayf(pl3, pl4, subs(CURVES=POLYGONS,[pl 2, pl1]), tickmarks=evalf([[ex],[ey]],3), view=[0..5, 0..5], scaling=c onstrained);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 15 "Le cas du carr\351" }}{EXCHG {PARA 0 "" 0 "" {HYPERLNK 17 "" 2 "interface" "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "in terface(rtablesize=13);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 114 "jx:=7; kx:=4; Matrix(jx+5,kx+5, Matrix(jx,kx, fill=0), fill=``) : < < -3,-2,-1,0,1,2,3,nk,yn,sxj,ysxj,y2 > | % > : " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 140 " dat:= <<`` |9|4|1|0|nj|xn|syk|xsyk|x2 >, %> : \nfor j from 1 to 4 do dat[j+1,j+1]:=1; od: for j from 5 to jx do dat[j+1,j x-j+2]:=1; od: dat:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 717 "for j to jx do \n dat[j+1, kx+2]:= add(dat[j+1,k+1],k=1..kx); dat[j+1, k x+3]:=dat[j+1,1]*%; dat[j+1, kx+6]:=dat[j+1,1]*%; \n dat[j+1, kx+4]: = add(dat[j+1,k+1]*dat[1,k+1],k=1..kx); dat[j+1, kx+5]:=dat[j+1,1]*%; \+ \nod : \nfor k to kx do \n dat[jx+2, k+1]:= add(dat[j+1,k+1],j=1..jx) ; dat[jx+3, k+1]:=dat[1,k+1]*%; dat[jx+6, k+1]:=dat[1,k+1]*%; \n dat[ jx+4, k+1]:= add(dat[j+1,k+1]*dat[j+1,1],j=1..jx); dat[jx+5, k+1]:=dat [1,k+1]*%; \nod:\ndat[jx+2, kx+2]:= add(dat[j+1,kx+2],j=1..jx): \ndat[ jx+2, kx+6]:= add(dat[j+1,kx+6],j=1..jx): dat[jx+6, kx+2]:= add(dat[jx +6,k+1],k=1..kx): \ndat[jx+4, kx+3]:= add(dat[j+1,kx+3],j=1..jx):\ndat [jx+3, kx+4]:= add(dat[jx+3,k+1],k=1..kx):\ndat[jx+5, kx+5]:= add(dat[ jx+5,k+1],k=1..kx): \ndat;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "ex:= dat[jx+4, kx+3]/dat[jx+2,kx+2]; ey:= dat[jx+3, kx+4]/dat[jx+2 ,kx+2];" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "vx:= dat[jx+2, \+ kx+6]/dat[jx+2,kx+2]-ex^2; vy:= dat[jx+6, kx+2]/dat[jx+2,kx+2]-ey^2; e valf([[ex,vx], [ey, vy]]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "vxy:= dat[jx+5, kx+5]/dat[jx+2,kx+2]-ex*ey;" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 44 "aa:= vxy/vx*1.; correl:= vxy/sqrt(vx*vy*1.);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 205 "rx:=0.3/2: ry:=0.6/2: wi th(plots, polygonplot):\npl1:= seq(seq(plot([dat[j+1,1]+rx*cos(t)*sqrt (dat[j+1,k+1]), dat[1,k+1]+ry*sin(t)*sqrt(dat[j+1,k+1]),t=0..2*Pi],\n \+ numpoints=8, color=grey),k=1..kx),j=1..jx):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "pl2:= plot([ex+rx/2*cos(t), ey+ry/2*sin(t),t=0..2* Pi], color=black, numpoints=8):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 104 "pl3:= plot([ex,y,y=0..9], color=black, linestyle=24), plot([ x,ey,x=-3..+3], color=black, linestyle=24):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "pl4:= plot(aa*(x-ex)+ey,x=-3.2..3.2,numpoints=3, c olor=black, linestyle=36):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 85 "displayf(pl3, pl4, subs(CURVES=POLYGONS,[pl2, pl1]), tickmarks=eva lf([[ex],[ey]],3));" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }} }{SECT 0 {PARA 3 "" 0 "" {TEXT -1 48 "Loi normale : d\351rivation depu is la loi binomiale" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "tmp:= sigma*fac(n)/fac(k)/fac(j)*p^j*q^k;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "stir:= fac=unapply(n^(n+1/2)/e^n*a,n);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 87 "(xcombipo@eval@subs)(stir,tmp); tmp 2:= subs(k+j-n=0, sigma=sqrt(n)*sqrt(p)*sqrt(q), %);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 77 "tmpj:= n^(1/2+j)*j^(-1/2-j)*p^(j+1/2);\nt mpk:= n^(1/2+k)*k^(-1/2-k)*q^(k+1/2);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "test:= \+ 'tmpj'*'tmpk'/a='tmp2'; (xcombipo@(lhs/rhs))(%): subs(j=n-k,%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 78 "(factor@simplify)(ln(tmpj),l n,symbolic); ln_tmpj:= map(combine,%,ln,symbolic);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "sigma=sqrt(n*p*q): val_n:= (op@solve)(%,\{n \});" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 39 "j=n*p+sigma*x: val_j:= subs (val_n, %); " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "(normal@sub s)(val_n, val_j, ln_tmpj); qqj:=series(%,sigma=infinity,4);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 28 "qqk:= subs(q=p, x=-x, qqj); \+ " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "defq:= p+q=1;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "(series)(qqj+qqk, sigma=inf inity); collect(%, [sigma, x], factor);\nsubs(defq, -1/2*defq, %): ser := collect(%, [sigma], factor);" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 20 "L'int\351gra le de Gauss" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 88 "G:= Int(exp(- x^2/2),x=-infinity..+infinity);\nG*subs(x=y,G); Doubleint(map2(op,1,%) ,x,y);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 92 "cte:= evalf(1/sqr t(2*Pi),2); pln:= plot(exp(-x^ 2/2)*cte, x=-5..5, color=red, linestyle =24):" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 10 "Un exemple" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "k:='k': nn,pp,qq:=20,0.1,1-'pp'; bin:= unapply(binomi al(nn,k)*pp^k*qq^(nn-k), k);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "li:= [seq(Weight(k-1/2..k+1/2, bin(k)),k=0..nn)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "pl1:= displayf(histogram(li), axes= boxed, tickmarks=[[0,nn*pp,nn],[0,evalf(bin(nn*pp),2)]]): %;" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "sig:= sqrt(nn*pp*qq); pl2:= \+ plottools[transform]((x,y)-> [(x-nn*pp)/sig, y*sig])(pl1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "displayf(pln, pl2, tickmarks=[[-2,0 ,2],[cte]], view=[-3..3, DEFAULT]);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 16 "Un autre exemple" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "nn,pp,qq:=80,0.1,1-'pp'; bin:= unapply(binomial(nn,k)*pp^k*qq^(n n-k), k);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "li:= [seq(Weig ht(k-1/2..k+1/2, bin(k)),k=0..nn)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "pl1:= displayf(histogram(li), axes=boxed, tickmarks=[ [0,nn*pp,nn],[0,evalf(bin(nn*pp),2)]]): %;" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 86 "sig:= sqrt(nn*pp*qq); pl2:= plottools[transform]((x ,y)-> [(x-nn*pp)/sig, y*sig])(pl1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "displayf(pln, pl2, tickmarks=[[-2,0,2],[cte]], view=[ -3..3, DEFAULT]);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 20 "Un troisie me exemple" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 73 "nn,pp,qq:=10,0 .5,1-'pp'; bin:= unapply(binomial(nn,k)*pp^k*qq^(nn-k), k);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "li:= [seq(Weight(k-1/2..k+1/ 2, bin(k)),k=0..nn)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 95 "pl 1:= displayf(histogram(li), axes=boxed, tickmarks=[[0,nn*pp,nn],[0,eva lf(bin(nn*pp),2)]]): %;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 " sig:= sqrt(nn*pp*qq); pl2:= plottools[transform]((x,y)-> [(x-nn*pp)/si g, y*sig])(pl1):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 70 "display f(pln, pl2, tickmarks=[[-2,0,2],[cte]], view=[-3..3, DEFAULT]);" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 0 "" }}}}{MARK "0 0 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }