{VERSION 5 0 "HP RISC UNIX" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 1 } {CSTYLE "" -1 257 "" 1 14 0 0 0 0 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 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "Helvet ica" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 258 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 260 1 {CSTYLE " " -1 -1 "" 1 14 0 0 0 0 1 1 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 263 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 264 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 31 "12. \334bungsblatt Compu teralgebra" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 257 "" 0 "" {TEXT 256 10 "Aufgabe 1:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "with(linalg):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "zuf := ra nd(0..9);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 126 "for i to 10 d o\nn[i] := 0;\nfor j to 100 do\nA := matrix(2,2,[seq(zuf(), i=1..4)]); \nif det(A) = 0 then n[i] := n[i] + 1 fi\nod\nod:" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 19 "seq(n[i], i=1..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "mittel := add(n[i], i=1..10)/10; evalf(%);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "sigma := sqrt(add((n[i]-mitt el)^2, i=1..10)/9);\nevalf(%);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 155 "N := 0:\nfor a from 0 to 9 do\nfor b from 0 to 9 do\nfor c fr om 0 to 9 do\nfor d from 0 to 9 do\nif det(matrix([[a,b],[c,d]])) = 0 \+ then N := N+1 fi\nod od od od;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "evalf(N/100);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 2 "N; " }}}{EXCHG {PARA 258 "" 0 "" {TEXT 257 10 "Aufgabe 2:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 62 "zuf := rand(0..10^11);\nzufzahl := \+ () -> evalf(zuf()*10^(-11));" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "summe := proc()\nlocal i;\nadd(zufzahl()^2, i=1..100);\nend;" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 298 "for k from 0 to 100 do n[k ] := 0 od:\nMinimum := 100: Maximum := 0:\nfor i to 1000 do\nk := floo r(summe());\nif k < Minimum then Minimum := k fi;\nif k > Maximum then Maximum := k fi;\nn[k] := n[k] + 1\nod:\nplots[display](seq(\nplottoo ls[rectangle]([k,0], [k+0.8,n[k]], color=blue),\nk=Minimum..Maximum)); \n" }}}{EXCHG {PARA 259 "" 0 "" {TEXT -1 10 "Aufgabe 3:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "restart:\nzufzahl \+ := rand(1..4);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 666 "Weg := p roc(Farbe)\nlocal Liste, i, j, x, y, xneu, yneu;\nx := 0: y := 0; List e := [0, 0];\nfor i to 50 do\nj := zufzahl();\n if j=1 then xneu := x +1; yneu := y;\n if xneu>10 then break fi;\nelif j=2 then xneu := x-1; yneu := y;\n if xneu<-10 then break fi;\nel if j=3 then xneu := x; yneu := y+1;\n if yneu>10 then bre ak fi;\nelse xneu := x; yneu := y-1;\n if yneu<-10 then break fi; \nfi;\nListe := Liste, [xneu, yneu];\nx := xneu; y := yneu;\nod;\nif a bs(xneu)>10 or abs(yneu)>10 then\nplot([Liste], color=Farbe, thickness =3), plottools[disk]([(x+xneu)/2, (y+yneu)/2], 0.5, color=blue)\nelse \+ plot([Liste], color=Farbe, thickness=3) fi;\nend;" }}}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 219 "plots[display](\nseq(seq(plottools[rectangl e]([i+0.15, j+0.15],[i+0.85, j+0.85], style=line, color=black),\ni =-1 0..9), j=-10..9),\nWeg(red), Weg(green), Weg(blue), Weg(cyan), Weg(mag enta), scaling=constrained, axes=none);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 491 "Weg2 := proc()\nlocal i, j, x, y, xneu, yneu;\nx := \+ 0: y := 0;\nfor i to 50 do\nj := zufzahl();\n if j=1 then xneu := x+1 ; yneu := y;\n if xneu>10 then break fi;\nelif j=2 then x neu := x-1; yneu := y;\n if xneu<-10 then break fi;\nelif j=3 then xneu := x; yneu := y+1;\n if yneu>10 then break fi;\nelse xneu := x; yneu := y-1;\n if yneu<-10 then break fi;\nf i;\nx := xneu; y := yneu;\nod;\nif abs(xneu)>10 or abs(yneu)>10 then\n \"Platsch\"\nelse [xneu, yneu] fi;\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 368 "Bad := 0:\nSx := 0: Sy := 0: Sr := 0: Sr2 := 0:\nfor i to 1000 do\nP := Weg2();\nif P=\"Platsch\" then Bad := Bad+1\nelse \+ Sx := Sx + P[1]; Sy := Sy + P[2];\nSr := Sr + sqrt(P[1]^2 + P[2]^2);\n Sr2 := Sr2 + P[1]^2 + P[2]^2;\nfi;\nod:\nN := 1000 - Bad;\nMittel := e valf([Sx/N, Sy/N]);\nEntfernungsmittel := evalf(Sr/N);\nStandardabweic hung := evalf(sqrt((Sr2/N - Entfernungsmittel^2)));" }}}{EXCHG {PARA 260 "" 0 "" {TEXT -1 10 "Aufgabe 4:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 261 "" 0 "" {TEXT -1 3 "a) " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "add(binomial(10, n)*0.55^n*0.45^(10-n), n=6..10);" }}}{EXCHG {PARA 262 "" 0 "" {TEXT -1 2 "b)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "aufgabe := rand(1..200);" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 101 "pruefung := proc()\nlocal i, n;\nn := 0;\nfor i to 10 do\nif aufgabe() <= 110 then n := n+1 fi\nod;\nn\nend;" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 232 "for n from 0 to 10 do Anzahl[n] := 0 od:\nfor i to 100 do\nn := pruefung(); Anzahl[n] := Anzahl[n]+1\nod :\nplots[display](seq(plottools[rectangle]([n-0.4, 0], [n+0.4, Anzahl[ n]], color=blue, style=patchnogrid), n=0..10), xtickmarks=10);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "Bestanden := add(Anzahl[n], \+ n=6..10);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "theoretischer_ Wert := 100*add(binomial(10, n)*0.55^n*0.45^(10-n), n=6..10);" }}} {EXCHG {PARA 263 "" 0 "" {TEXT -1 2 "c)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 93 "W := 0:\nfor i to 100 do\nif pruefu ng() < 6 then\nif pruefung() >= 6 then W := W+1 fi\nfi\nod:\nW;\n" }}} {EXCHG {PARA 264 "" 0 "" {TEXT -1 2 "d)" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 64 "readlib(randomize): # nur bei \344 lteren Maple-Versionen notwendig" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 81 "do\nStartwert := _seed;\nif pruefung() = 10 then brea k fi\nod:\nrandomize(Startwert):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "pruefung();" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "pruefung();" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}} {MARK "2 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }