{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 "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "" 0 1 0 0 255 1 0 0 0 0 0 0 0 0 0 1 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Output" 0 11 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 3 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "T itle" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 0 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }{PSTYLE "Author" 0 19 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 8 8 0 0 0 0 0 0 -1 0 } } {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 45 "Example 6: Understanding \+ an Important Theorem" }}{PARA 19 "" 0 "" {TEXT -1 15 "by Zavan Karian " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 83 "restart: with(plots, di splay): libname:=\"C:/mylib/statistics\",libname: with(stat):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "f := x -> (3/2)*x^2;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrowG F(,$*$)9$\"\"#\"\"\"#\"\"$F0F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "int(f(x), x=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#\"\"\"" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "mu := int(x*f(x ), x=-1..1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#muG\"\"!" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "var := int(x^2*f(x), x=-1..1 )- mu^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$varG#\"\"$\"\"&" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "F := int(f(t), t=-1..x);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"FG,&*$)%\"xG\"\"$\"\"\"#F*\"\"#F+F *" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "A := ContinuousS(f(x), -1..1, 5);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"AG7'$!+r)Q?C&!#5$!+ +9s&4(F($!+e$ylx'F($!+.kR>PF($\"+;(ek)[F(" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 35 "A := ContinuousS(f(x), -1..1, 400):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "H := Histogram(A, -1..1, 12):" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "P := plot(f(x), x=-1..1):" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "display(\{P,H\});" }} {PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7S7$ $!\"\"\"\"!$\"3++++++++:!#<7$$!3ommm;p0k&*!#=$\"3k#fy0xn?P\"F-7$$!3wKL $3(zdJRl7F-7$$!3mmmmT%p\"e()F1$\"37dT`zHe]6F-7$$!3:mmm\" 4m(G$)F1$\"3YYa9p^_S5F-7$$!3\"QLL3i.9!zF1$\"3?s%HaF1$\"3NXA,U_(=U%F17$$!3Q+++]$*4)* \\F1$\"3+k0(oc\\ru$F17$$!39+++]_&\\c%F1$\"3l%Qv^YAe7$F17$$!31+++]1aZTF 1$\"3Ij.^;SJ!e#F17$$!3umm;/#)[oPF1$\"3;'\\T<]D-8#F17$$!3hLLL$=exJ$F1$ \"3K&HhW!z7^;F17$$!3*RLLLtIf$HF1$\"3;\"oR1R`HH\"F17$$!3]++]PYx\"\\#F1$ \"3d(QKhE6MJ*!#>7$$!3EMLLL7i)4#F1$\"3M(G'\\@mJ1mFcq7$$!3c****\\P'psm\" F1$\"3#*pS>m?opTFcq7$$!3')****\\74_c7F1$\"3Y[ZK0sEoBFcq7$$!3)3LLL3x%z# )Fcq$\"35F;g6hCG5Fcq7$$!3KMLL3s$QM%Fcq$\"3Tq^(QDQ.$G!#?7$$!3]^omm;zr)* !#@$\"3O'4^11%yh9!#B7$$\"3%pJL$ezw5VFcq$\"31z*)ee!3uy#F]s7$$\"3s*)*** \\PQ#\\\")Fcq$\"3+se)Q\"H^h**F]s7$$\"3GKLLe\"*[H7F1$\"3y3))o&QluE#Fcq7 $$\"3I*******pvxl\"F1$\"3IJdE2/LATFcq7$$\"3#z****\\_qn2#F1$\"3U\\JE?PY pkFcq7$$\"3U)***\\i&p@[#F1$\"3$3:-bg[2/a(*G\"F17$$\"3ElmmmZvOLF1$\"3'o!4$f&)*3q;F17$$\"3i******\\2goPF1$ \"3+%3N>u_.8#F17$$\"3UKL$eR<*fTF1$\"3A;N-6pt&f#F17$$\"3m******\\)Hxe%F 1$\"31`r[w(*3dJF17$$\"3ckm;H!o-*\\F1$\"3%>WQ/D;at$F17$$\"3y)***\\7k.6a F1$\"3YG,hes*=R%F17$$\"3#emmmT9C#eF1$\"3Cv6\"fWw]3&F17$$\"33****\\i!*3 `iF1$\"3snN`B%o^'eF17$$\"3%QLLL$*zym'F1$\"33,C!3U$4pmF17$$\"3wKLL3N1#4 (F1$\"3M&*\\$4s/Ya(F17$$\"3Nmm;HYt7vF1$\"35,?CTs\")f$*F17$$\"3]mmmT6KU$)F1$\"3]z/YI[\"R/\"F-7$$\"3fKL LLbdQ()F1$\"33zlFN0WX6F-7$$\"3[++]i`1h\"*F1$\"31f*R'yn()e7F-7$$\"3W++] P?Wl&*F1$\"3Q#e\"f?_Ys8F-7$$\"\"\"F*F+-%'COLOURG6&%$RGBG$\"#5F)$F*F*Fa [l-F$6%7R7$F(Fa[l7$F($\"3))************z8F-7$$!3qLLLLLLL$)F1Fg[l7$Fj[l Fa[lF\\\\l7$Fj[l$\"3k*************f*F17$$!3ImmmmmmmmF1F^\\l7$Fa\\lFa[l Fc\\l7$Fa\\l$\"35+++++++XF17$$!3++++++++]F1Fe\\l7$Fh\\lFa[lFj\\l7$Fh\\ l$\"31++++++]AF17$$!3:LLLLLLLLF1F\\]l7$F_]lFa[lFa]l7$F_]l$\"3!******** *******HFcq7$$!3emmmmmmm;F1Fc]l7$Ff]lFa[lFh]lFh]l7$Fa[lFa[lFi]lFi]lFi] l7$$\"3emmmmmmm;F1Fa[lFj]lFj]l7$F[^l$\"3s*************\\(Fcq7$$\"3:LLL LLLLLF1F^^l7$Fa^lFa[lFc^l7$Fa^l$\"33++++++]>F17$$\"3++++++++]F1Fe^l7$F h^lFa[lFj^l7$Fh^l$\"3w**************fF17$$\"3ImmmmmmmmF1F\\_l7$F__lFa[ lFa_l7$F__l$\"3a+++++++\")F17$$\"3qLLLLLLL$)F1Fc_l7$Ff_lFa[lFh_l7$Ff_l $\"3#************\\F\"F-7$FizFj_l7$FizFa[l-F\\[l6&F^[l$\"*++++\"!\")Fa [lFa[l-%*LINESTYLEG6#\"\"$-%+AXESLABELSG6%Q\"x6\"Q!6\"%(DEFAULTG-%%VIE WG6$;F(FizF^al" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "S4 := [seq(ContinuousS(f(x ), -1..1, 4), i=1..300)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "S4[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#7&$!+K5R=o!#5$\"+#=F!o()F&$ \"+YnV4$*F&$\"+.45?')F&" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 " M4 := [seq(Mean(S4[i]), i=1..300)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "H4 := Histogram(M4, -1..1, 7):" }}}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 30 "n4 := NormalPDF(mu, var/4, x):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "N4 := plot(n4, x=-1..1, color=blue) :" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "# interface(plotdevice =postscript, plotoutput=Fig6a);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "display(\{P, H4, N4\});" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6$7S7$$!\"\"\"\"!$\"3++++++++:!#<7$$!3omm m;p0k&*!#=$\"3k#fy0xn?P\"F-7$$!3wKL$3(zdJRl7F-7$$!3mmmmT %p\"e()F1$\"37dT`zHe]6F-7$$!3:mmm\"4m(G$)F1$\"3YYa9p^_S5F-7$$!3\"QLL3i .9!zF1$\"3?s%H aF1$\"3NXA,U_(=U%F17$$!3Q+++]$*4)*\\F1$\"3+k0(oc\\ru$F17$$!39+++]_&\\c %F1$\"3l%Qv^YAe7$F17$$!31+++]1aZTF1$\"3Ij.^;SJ!e#F17$$!3umm;/#)[oPF1$ \"3;'\\T<]D-8#F17$$!3hLLL$=exJ$F1$\"3K&HhW!z7^;F17$$!3*RLLLtIf$HF1$\"3 ;\"oR1R`HH\"F17$$!3]++]PYx\"\\#F1$\"3d(QKhE6MJ*!#>7$$!3EMLLL7i)4#F1$\" 3M(G'\\@mJ1mFcq7$$!3c****\\P'psm\"F1$\"3#*pS>m?opTFcq7$$!3')****\\74_c 7F1$\"3Y[ZK0sEoBFcq7$$!3)3LLL3x%z#)Fcq$\"35F;g6hCG5Fcq7$$!3KMLL3s$QM%F cq$\"3Tq^(QDQ.$G!#?7$$!3]^omm;zr)*!#@$\"3O'4^11%yh9!#B7$$\"3%pJL$ezw5V Fcq$\"31z*)ee!3uy#F]s7$$\"3s*)***\\PQ#\\\")Fcq$\"3+se)Q\"H^h**F]s7$$\" 3GKLLe\"*[H7F1$\"3y3))o&QluE#Fcq7$$\"3I*******pvxl\"F1$\"3IJdE2/LATFcq 7$$\"3#z****\\_qn2#F1$\"3U\\JE?PYpkFcq7$$\"3U)***\\i&p@[#F1$\"3$3:-bg[ 2/a(*G\"F17$$\"3ElmmmZvOLF1$\"3'o!4 $f&)*3q;F17$$\"3i******\\2goPF1$\"3+%3N>u_.8#F17$$\"3UKL$eR<*fTF1$\"3A ;N-6pt&f#F17$$\"3m******\\)Hxe%F1$\"31`r[w(*3dJF17$$\"3ckm;H!o-*\\F1$ \"3%>WQ/D;at$F17$$\"3y)***\\7k.6aF1$\"3YG,hes*=R%F17$$\"3#emmmT9C#eF1$ \"3Cv6\"fWw]3&F17$$\"33****\\i!*3`iF1$\"3snN`B%o^'eF17$$\"3%QLLL$*zym' F1$\"33,C!3U$4pmF17$$\"3wKLL3N1#4(F1$\"3M&*\\$4s/Ya(F17$$\"3Nmm;HYt7vF 1$\"35,?CTs\")f$*F17$$\"3]mmmT6 KU$)F1$\"3]z/YI[\"R/\"F-7$$\"3fKLLLbdQ()F1$\"33zlFN0WX6F-7$$\"3[++]i`1 h\"*F1$\"31f*R'yn()e7F-7$$\"3W++]P?Wl&*F1$\"3Q#e\"f?_Ys8F-7$$\"\"\"F*F +-%'COLOURG6&%$RGBG$\"#5F)$F*F*Fa[l-F$6%7>7$F(Fa[l7$F($\"3smmmmmm;:F17 $$!3,Vr&G9dG9(F1Fg[l7$Fj[lFa[lF\\\\l7$Fj[l$\"3WLLLLLLLIF17$$!3[&G9dG9d G%F1F^\\l7$Fa\\lFa[lFc\\l7$Fa\\l$\"3_LLLLLL$)oF17$$!3\\G9dG9dG9F1Fe\\l 7$Fh\\lFa[lFj\\l7$Fh\\l$\"3TLLLLLL.5F-7$$\"3\\G9dG9dG9F1F\\]l7$F_]lFa[ lFa]l7$F_]l$\"3NLLLLLLLzF17$$\"3[&G9dG9dG%F1Fc]l7$Ff]lFa[lFh]l7$Ff]l$ \"3]LLLLLLLPF17$$\"3,Vr&G9dG9(F1Fj]l7$F]^lFa[lF_^l7$F]^l$\"3ummmmmmm=F 17$FizFa^l7$FizFa[l-F\\[l6&F^[l$\"*++++\"!\")Fa[lFa[l-%*LINESTYLEG6#\" \"$-F$6$7W7$F($\"3?JT=]:luOFcq7$F/$\"3U>jrUF'H)[Fcq7$F5$\"39ZX\\mi?*=' Fcq7$F:$\"3q_AO58+))zFcq7$F?$\"3[2Hx%HG,-\"F17$FD$\"3eE\\[:A[&G\"F17$F I$\"3k$=dF17$FS$\"3%**>B^&\\APBF17$FX$\"3( HWwRt.T!GF17$Fgn$\"3wyFk&*H,SLF17$F\\o$\"3w>)Gt(zvbQF17$Fao$\"3'y6gvcy %zWF17$Ffo$\"3IC#\\%zcqU^F17$F[p$\"3(fNf)3m[0eF17$F`p$\"3K7=5q6=;kF17$ Fep$\"3%zz$o\"fwp8(F17$Fjp$\"3'RVo[te#GxF17$F_q$\"3gli\\!yA\\P)F17$Feq $\"3q>b6@7?%*))F17$Fjq$\"3q&\\;(4m2*Q*F17$F_r$\"3am_w_$fDx*F17$Fdr$\"3 $)*G+W_%z15F-7$$!3gKL$e9d;J'Fcq$\"3t)4dAswk,\"F-7$Fir$\"3\\MD$[81O-\"F -7$$!3T,+]ivF@AFcq$\"3MK$4Hzr$G5F-7$F_s$\"3n(*Hm#>h+.\"F-7$$\"3@CL$3-D g5#Fcq$\"3>eS(zwU&G5F-7$Ffs$\"3X.-'>z.P-\"F-7$$\"3L`mmmJ+IiFcq$\"3sbXy kP#o,\"F-7$F[t$\"37?]tWG^25F-7$F`t$\"3](y\"[<[Z%z*F17$Fet$\"3O;yu]:'*) R*F17$Fjt$\"3sZCa?7H@*)F17$F_u$\"3izPC+0F)Q)F17$Fdu$\"3qRAwA_vLxF17$Fi u$\"3\\um'yImp5(F17$F^v$\"31ONI^(**fT'F17$Fcv$\"3-me>lMi&y&F17$Fhv$\"3 j?ZZ;l42^F17$F]w$\"3)fJllht6\\%F17$Fbw$\"3[eb,9*H:)QF17$Fgw$\"39\"R8l \\%RFLF17$F\\x$\"3/iqT2n!yz#F17$Fax$\"3k>N5!e\"3SBF17$Ffx$\"34Y@_d8NE> F17$F[y$\"3UuTmR/ip:F17$F`y$\"3w$=%y)f:pG\"F17$Fey$\"3La:YkHZ75F17$Fjy $\"3%3&f())**3)z!)Fcq7$F_z$\"3/M*eRD$[ziFcq7$Fdz$\"3A(ok`!>ly[Fcq7$Fiz Fb_l-F\\[l6&F^[lFa[lFa[lFg^l-%+AXESLABELSG6%Q\"x6\"Q!6\"%(DEFAULTG-%%V IEWG6$;F(FizF_jl" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" }}}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "S8 := [ seq(ContinuousS(f(x), -1..1, 8), i=1..300)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "A[1];" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#$\"+Ap_$*y!#5 " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "M8 := [seq(Mean(S8[i]), i=1..300)]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "# interface (plotdevice=postscript, plotoutput=Fig6b);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 30 "H8 := Histogram(M8, -1..1, 7):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 30 "n8 := NormalPDF(mu, var/8, x):" }}{PARA 0 "> " 0 " " {MPLTEXT 1 0 36 "N8 := plot(n8, x=-1..1, color=blue):" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 21 "display(\{P, H8, N8\});" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6$7S7$$!\"\"\"\"!$\"3++ ++++++:!#<7$$!3ommm;p0k&*!#=$\"3k#fy0xn?P\"F-7$$!3wKL$3( zdJRl7F-7$$!3mmmmT%p\"e()F1$\"37dT`zHe]6F-7$$!3:mmm\"4m(G$)F1$\"3YYa9p ^_S5F-7$$!3\"QLL3i.9!zF1$\"3?s%HaF1$\"3NXA,U_(=U%F17$$!3Q+++]$*4)*\\F1$\"3+k0(oc\\ru $F17$$!39+++]_&\\c%F1$\"3l%Qv^YAe7$F17$$!31+++]1aZTF1$\"3Ij.^;SJ!e#F17 $$!3umm;/#)[oPF1$\"3;'\\T<]D-8#F17$$!3hLLL$=exJ$F1$\"3K&HhW!z7^;F17$$! 3*RLLLtIf$HF1$\"3;\"oR1R`HH\"F17$$!3]++]PYx\"\\#F1$\"3d(QKhE6MJ*!#>7$$ !3EMLLL7i)4#F1$\"3M(G'\\@mJ1mFcq7$$!3c****\\P'psm\"F1$\"3#*pS>m?opTFcq 7$$!3')****\\74_c7F1$\"3Y[ZK0sEoBFcq7$$!3)3LLL3x%z#)Fcq$\"35F;g6hCG5Fc q7$$!3KMLL3s$QM%Fcq$\"3Tq^(QDQ.$G!#?7$$!3]^omm;zr)*!#@$\"3O'4^11%yh9!# B7$$\"3%pJL$ezw5VFcq$\"31z*)ee!3uy#F]s7$$\"3s*)***\\PQ#\\\")Fcq$\"3+se )Q\"H^h**F]s7$$\"3GKLLe\"*[H7F1$\"3y3))o&QluE#Fcq7$$\"3I*******pvxl\"F 1$\"3IJdE2/LATFcq7$$\"3#z****\\_qn2#F1$\"3U\\JE?PYpkFcq7$$\"3U)***\\i& p@[#F1$\"3$3:-bg[2/a(*G\"F17$$\"3El mmmZvOLF1$\"3'o!4$f&)*3q;F17$$\"3i******\\2goPF1$\"3+%3N>u_.8#F17$$\"3 UKL$eR<*fTF1$\"3A;N-6pt&f#F17$$\"3m******\\)Hxe%F1$\"31`r[w(*3dJF17$$ \"3ckm;H!o-*\\F1$\"3%>WQ/D;at$F17$$\"3y)***\\7k.6aF1$\"3YG,hes*=R%F17$ $\"3#emmmT9C#eF1$\"3Cv6\"fWw]3&F17$$\"33****\\i!*3`iF1$\"3snN`B%o^'eF1 7$$\"3%QLLL$*zym'F1$\"33,C!3U$4pmF17$$\"3wKLL3N1#4(F1$\"3M&*\\$4s/Ya(F 17$$\"3Nmm;HYt7vF1$\"35,?CTs\") f$*F17$$\"3]mmmT6KU$)F1$\"3]z/YI[\"R/\"F-7$$\"3fKLLLbdQ()F1$\"33zlFN0W X6F-7$$\"3[++]i`1h\"*F1$\"31f*R'yn()e7F-7$$\"3W++]P?Wl&*F1$\"3Q#e\"f?_ Ys8F-7$$\"\"\"F*F+-%'COLOURG6&%$RGBG$\"#5F)$F*F*Fa[l-F$6%7>7$F(Fa[lFe[ l7$$!3,Vr&G9dG9(F1Fa[lFf[lFf[l7$Fg[l$\"3ymmmmmm;AF17$$!3[&G9dG9dG%F1Fj [l7$F]\\lFa[lF_\\l7$F]\\l$\"3_mmmmmmm\")F17$$!3\\G9dG9dG9F1Fa\\l7$Fd\\ lFa[lFf\\l7$Fd\\l$\"3cmmmmmmT8F-7$$\"3\\G9dG9dG9F1Fh\\l7$F[]lFa[lF]]l7 $F[]l$\"3o*************R)F17$$\"3[&G9dG9dG%F1F_]l7$Fb]lFa[lFd]l7$Fb]l$ \"3'*************\\CF17$$\"3,Vr&G9dG9(F1Ff]l7$Fi]lFa[lF[^l7$Fi]l$\"3K+ ++++++NFcq7$FizF]^l7$FizFa[l-F\\[l6&F^[l$\"*++++\"!\")Fa[lFa[l-%*LINES TYLEG6#\"\"$-F$6$7[o7$F($\"3+>j\\;a)Q&=F]s7$F/$\"3Oe=Pqz`tKF]s7$F5$\"3 'Rb0@a4#f_F]s7$F:$\"3ej-V#4e/w)F]s7$F?$\"3ujDZZGwG9Fcq7$FD$\"3gZ'\\.WH (oAFcq7$FI$\"3@-xG,Q=3MFcq7$FN$\"3'R)**>2D)43&Fcq7$FS$\"3[fjglH$)*\\(F cq7$FX$\"3-KS\"e$*R&z5F17$Fgn$\"3NV4@]`gJ:F17$F\\o$\"3&R0pzIF6/#F17$Fa o$\"3%*)f%[qx*[v#F17$Ffo$\"3MLf#G)R1JOF17$F[p$\"3K]IC/&H#F1$\"37_e*fe9`-\"F-7$Feq$\"37b\\S=m3'3\"F-7$Fjq$ \"3m?Zsy\"4.@\"F-7$F_r$\"35l-3IZ>68F-7$Fdr$\"3#e%=aPrl\"R\"F-7$$!3gKL$ e9d;J'Fcq$\"3)R#)Qdd_&=9F-7$Fir$\"3D$=qDQ@&Q9F-7$$!3'ym;aQdDG$Fcq$\"3w \"*)3BP/jW\"F-7$$!3T,+]ivF@AFcq$\"3o@lfmt%>X\"F-7$$!3'\\L$eRx**f6Fcq$ \"3)yx+o/DaX\"F-7$F_s$\"3!oO-nx@nX\"F-7$$\"3&yK$3_Nl.5Fcq$\"3)RJUdI`dX \"F-7$$\"3@CL$3-Dg5#Fcq$\"3!R;QD?ICX\"F-7$$\"3e?Le*['R3KFcq$\"3Ibk#**e onW\"F-7$Ffs$\"3\"f&[))zezQ9F-7$$\"3L`mmmJ+IiFcq$\"3v5iGx8_>9F-7$F[t$ \"3)fe/XmVOR\"F-7$F`t$\"3DO)fn;#3<8F-7$Fet$\"3W;r\\y*eG@\"F-7$Fjt$\"3- XGH4Fr#4\"F-7$$\"3=)**\\P/q%zAF1$\"3#=%>K%[W-.\"F-7$F_u$\"3Eruv3oSg'*F 17$$\"3L)**\\(=GB2FF1$\"3$=k`?hdn$*)F17$Fdu$\"3xWQJ\\%o;@)F17$$\"3uJL$ 3UDX8$F1$\"3q(fqZ))[nc(F17$Fiu$\"3T2W=FEcMpF17$F^v$\"33*GI/z,P`b,$pFF17$Fbw$\"3) z+81M/&o?F17$Fgw$\"3=C+:lW0?:F17$F\\x$\"3Y+o1\\opu5F17$Fax$\"3ZnjS,s<= vFcq7$Ffx$\"3U$[dUjMZ4&Fcq7$F[y$\"3[kcxWf^#Q$Fcq7$F`y$\"3s*)\\7xAv8aF]s 7$Fdz$\"3EX'o9bgxE$F]s7$FizF^_l-F\\[l6&F^[lFa[lFa[lFc^l-%+AXESLABELSG6 %Q\"x6\"Q!6\"%(DEFAULTG-%%VIEWG6$;F(FizF]]m" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" }}}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 51 "A := [seq(ContinuousS(f(x), -1..1, 16), i=1..300)]: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "M16 := [seq(Mean(A[i]), i=1..300)]:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "H16 := Histogram(M1 6, -1..1, 13):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 32 "n16 := NormalPDF( mu, var/16, x):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 38 "N16 := plot(n16, x=-1..1, color=blue):" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "display( \{P, H16, N16\});" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6'-%'CURVESG6$7S7$$!\"\"\"\"!$\"3++++++++:!#<7$$!3ommm;p0k&*!#=$\"3 k#fy0xn?P\"F-7$$!3wKL$3(zdJRl7F-7$$!3mmmmT%p\"e()F1$\"37 dT`zHe]6F-7$$!3:mmm\"4m(G$)F1$\"3YYa9p^_S5F-7$$!3\"QLL3i.9!zF1$\"3?s%HaF1$\"3NXA,U_( =U%F17$$!3Q+++]$*4)*\\F1$\"3+k0(oc\\ru$F17$$!39+++]_&\\c%F1$\"3l%Qv^YA e7$F17$$!31+++]1aZTF1$\"3Ij.^;SJ!e#F17$$!3umm;/#)[oPF1$\"3;'\\T<]D-8#F 17$$!3hLLL$=exJ$F1$\"3K&HhW!z7^;F17$$!3*RLLLtIf$HF1$\"3;\"oR1R`HH\"F17 $$!3]++]PYx\"\\#F1$\"3d(QKhE6MJ*!#>7$$!3EMLLL7i)4#F1$\"3M(G'\\@mJ1mFcq 7$$!3c****\\P'psm\"F1$\"3#*pS>m?opTFcq7$$!3')****\\74_c7F1$\"3Y[ZK0sEo BFcq7$$!3)3LLL3x%z#)Fcq$\"35F;g6hCG5Fcq7$$!3KMLL3s$QM%Fcq$\"3Tq^(QDQ.$ G!#?7$$!3]^omm;zr)*!#@$\"3O'4^11%yh9!#B7$$\"3%pJL$ezw5VFcq$\"31z*)ee!3 uy#F]s7$$\"3s*)***\\PQ#\\\")Fcq$\"3+se)Q\"H^h**F]s7$$\"3GKLLe\"*[H7F1$ \"3y3))o&QluE#Fcq7$$\"3I*******pvxl\"F1$\"3IJdE2/LATFcq7$$\"3#z****\\_ qn2#F1$\"3U\\JE?PYpkFcq7$$\"3U)***\\i&p@[#F1$\"3$3:-bg[2/a(*G\"F17$$\"3ElmmmZvOLF1$\"3'o!4$f&)*3q;F17$$\" 3i******\\2goPF1$\"3+%3N>u_.8#F17$$\"3UKL$eR<*fTF1$\"3A;N-6pt&f#F17$$ \"3m******\\)Hxe%F1$\"31`r[w(*3dJF17$$\"3ckm;H!o-*\\F1$\"3%>WQ/D;at$F1 7$$\"3y)***\\7k.6aF1$\"3YG,hes*=R%F17$$\"3#emmmT9C#eF1$\"3Cv6\"fWw]3&F 17$$\"33****\\i!*3`iF1$\"3snN`B%o^'eF17$$\"3%QLLL$*zym'F1$\"33,C!3U$4p mF17$$\"3wKLL3N1#4(F1$\"3M&*\\$4s/Ya(F17$$\"3Nmm;HYt7vF1$\"35,?CTs\")f$*F17$$\"3]mmmT6KU$)F1$\"3]z/YI [\"R/\"F-7$$\"3fKLLLbdQ()F1$\"33zlFN0WX6F-7$$\"3[++]i`1h\"*F1$\"31f*R' yn()e7F-7$$\"3W++]P?Wl&*F1$\"3Q#e\"f?_Ys8F-7$$\"\"\"F*F+-%'COLOURG6&%$ RGBG$\"#5F)$F*F*Fa[l-F$6%7V7$F(Fa[lFe[l7$$!3Yh%Q:YQ:Y)F1Fa[lFf[lFf[lFf [l7$$!3\"H#p2Bp2BpF1Fa[lFi[lFi[l7$Fj[l$\"3\\LLLLLLLVFcq7$$!3O%Q:YQ:YQ& F1F]\\l7$F`\\lFa[lFb\\l7$F`\\l$\"3-+++++++8F17$$!3OYQ:YQ:YQF1Fd\\l7$Fg \\lFa[lFi\\l7$Fg\\l$\"3)ommmmmm1'F17$$!3#yI#p2Bp2BF1F[]l7$F^]lFa[lF`]l 7$F^]l$\"3KLLLLLLy7F-7$$!3u#p2Bp2Bp(FcqFb]l7$Fe]lFa[lFg]l7$Fe]l$\"3tmm mmmm1>F-7$$\"3u#p2Bp2Bp(FcqFi]l7$F\\^lFa[lF^^l7$F\\^l$\"31++++++g:F-7$ $\"3#yI#p2Bp2BF1F`^l7$Fc^lFa[lFe^l7$Fc^l$\"3'pmmmmmmm)F17$$\"3OYQ:YQ:Y QF1Fg^l7$Fj^lFa[lF\\_l7$Fj^l$\"3OLLLLLL$3\"F17$$\"3O%Q:YQ:YQ&F1F^_l7$F a_lFa[lFc_lFc_l7$$\"3\"H#p2Bp2BpF1Fa[lFd_lFd_lFd_l7$$\"3Yh%Q:YQ:Y)F1Fa [lFg_lFg_lFg_l7$FizFa[lFj_l-F\\[l6&F^[l$\"*++++\"!\")Fa[lFa[l-%*LINEST YLEG6#\"\"$-F$6$7eo7$F($\"3R6$*fX%ylL$Fds7$F/$\"3)p#p*)*4G./\"!#A7$F5$ \"3UyGpC#*>&o#F]al7$F:$\"3S\\&*z/[c]uF]al7$F?$\"3e*fx^\">y\")>Fas7$FD$ \"3gx:hpO!p*\\Fas7$FI$\"3zOs&)Q)ow7\"F]s7$FN$\"3c:V@LzG1DF]s7$FS$\"3U% GTIkz0Y&F]s7$FX$\"3@H`L.\"\\^%[kr(F17$F_ q$\"3]/I>:PV-!*F17$$!3QnmTNz>&H#F1$\"3V$f%zOle?5F-7$Feq$\"3w-?tob:X6F- 7$$!3#pm;aVXH)=F1$\"3we5muN2%G\"F-7$Fjq$\"3z>.\\;P4A9F-7$$!3s*****\\F& *=Y\"F1$\"3U\"[&3`7K\\:F-7$F_r$\"3%GEBF-7$Fir$ \"3a(fv5uX*3?F-7$$!3'ym;aQdDG$Fcq$\"3;hM?')HuI?F-7$$!3T,+]ivF@AFcq$\"3 +))>Ub/iY?F-7$$!3=o;/^wj!p\"Fcq$\"3gy(=9&GH_?F-7$$!3'\\L$eRx**f6Fcq$\" 3evZHfiVc?F-7$$!3S<+D\"GyNH'F]s$\"3y%[JeOT!f?F-7$F_s$\"3K!Qj!4B5g?F-7$ $\"3o'H$3x\"yY_%F]s$\"3GIaz,ocf?F-7$$\"3&yK$3_Nl.5Fcq$\"3k2s)y)ROd?F-7 $$\"3/E$ekGR[b\"Fcq$\"3qp'pk@*\\`?F-7$$\"3@CL$3-Dg5#Fcq$\"3u#\\.K'=)z/ #F-7$$\"3e?Le*['R3KFcq$\"3%=7\"*H!o/K?F-7$Ffs$\"3Q1va/Dr4?F-7$$\"3L`mm mJ+IiFcq$\"3qE\"QD&yAc>F-7$F[t$\"3!*\\=2UVb&)=F-7$$\"3ilm\"z\\1A-\"F1$ \"3M\\dZ.q?#z\"F-7$F`t$\"3Gp'\\1^uSo\"F-7$$\"3ylm;HCjV9F1$\"3APMD:4G9F-7$$\"3g)***\\7JFn=F1$\"3g4OF,f<%H\"F-7$Fjt$\"3aB $>+7r\"f6F-7$$\"3=)**\\P/q%zAF1$\"3(eq]8YC/.\"F-7$F_u$\"3A[4=\"Qi*f!*F 17$$\"3L)**\\(=GB2FF1$\"3gis()y%fMv(F17$Fdu$\"3E:B+isLYlF17$$\"3uJL$3U DX8$F1$\"3)z4='RkXebF17$Fiu$\"3+zVgj2YoYF17$F^v$\"3?6'em$[%45$F17$Fcv$ \"3_*QR=8%R]?F17$Fhv$\"3,h6kZc*[C\"F17$F]w$\"3+kDCeZ>XuFcq7$Fbw$\"3-(z W_IFQ:%Fcq7$Fgw$\"3/sI])*p7VAFcq7$F\\x$\"3P59ogIE@6Fcq7$Fax$\"3=_#3(\\ \\K([&F]s7$Ffx$\"30>*zDF]s7$F[y$\"3IP&fiIZ26\"F]s7$F`y$\"3:%f9KEG #>]Fas7$Fey$\"3x!H'3'ygH#>Fas7$Fjy$\"3uf8z2&Q!*z(F]al7$F_z$\"3y?`')RyK XGF]al7$Fdz$\"3Z%3z3Afm.\"F]al7$FizFh`l-F\\[l6&F^[lFa[lFa[lF]`l-%+AXES LABELSG6%Q\"x6\"Q!6\"%(DEFAULTG-%%VIEWG6$;F(FizFjam" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" } }}}}{MARK "28 5" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }