%!PS-Adobe-2.0 %%Creator: dvips(k) 5.96dev Copyright 2007 Radical Eye Software %%Title: blatt5.dvi %%CreationDate: Fri Nov 14 08:24:54 2008 %%Pages: 1 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: SFRM1000 SFBX1440 SFRM1440 SFBX1000 CMMI10 CMR10 CMSY10 %%+ MSBM10 CMR7 CMMI7 CMR5 CMEX10 CMSY7 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -D600 blatt5.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2008.11.14:0824 %%BeginProcSet: tex.pro 0 0 %! /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{ landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[ matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{ statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0] N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub} B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr 1 add N}if}B/CharBuilder{save 3 1 roll S A/base get 2 index get S /BitMaps get S get/Cd X pop/ctr 0 N Cdx 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx sub Cy .1 sub]{Ci}imagemask restore}B/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{ bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{ SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{ userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{ /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT) (LaserWriter 16/600)]{A length product length le{A length product exch 0 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot} imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M} B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{ p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end %%EndProcSet %%BeginProcSet: cm-super-t1.enc 0 0 % This file is generated from `T1uni.map' and `glyphlist.txt', `gl-other.txt' % % LIGKERN hyphen hyphen =: endash ; 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TeXDict begin/rf{findfont dup length 1 add dict begin{1 index/FID ne 2 index/UniqueID ne and{def}{pop pop}ifelse}forall[1 index 0 6 -1 roll exec 0 exch 5 -1 roll VResolution Resolution div mul neg 0 0]/Metrics exch def dict begin Encoding{exch dup type/integertype ne{pop pop 1 sub dup 0 le{pop}{[}ifelse}{FontMatrix 0 get div Metrics 0 get div def} ifelse}forall Metrics/Metrics currentdict end def[2 index currentdict end definefont 3 -1 roll makefont/setfont cvx]cvx def}def/ObliqueSlant{ dup sin S cos div neg}B/SlantFont{4 index mul add}def/ExtendFont{3 -1 roll mul exch}def/ReEncodeFont{CharStrings rcheck{/Encoding false def dup[exch{dup CharStrings exch known not{pop/.notdef/Encoding true def} if}forall Encoding{]exch pop}{cleartomark}ifelse}if/Encoding exch def} def end %%EndProcSet %%BeginFont: CMSY7 %!PS-AdobeFont-1.1: CMSY7 1.0 %%CreationDate: 1991 Aug 15 07:21:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put readonly def /FontBBox{-15 -951 1252 782}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMEX10 %!PS-AdobeFont-1.1: CMEX10 1.00 %%CreationDate: 1992 Jul 23 21:22:48 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMEX10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMEX10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 26 /braceleftbigg put dup 56 /bracelefttp put dup 58 /braceleftbt put dup 60 /braceleftmid put dup 62 /braceex put readonly def /FontBBox{-24 -2960 1454 772}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR5 %!PS-AdobeFont-1.1: CMR5 1.00B %%CreationDate: 1992 Feb 19 19:55:02 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR5 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 50 /two put readonly def /FontBBox{-341 -250 1304 965}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI7 %!PS-AdobeFont-1.1: CMMI7 1.100 %%CreationDate: 1996 Jul 23 07:53:53 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 21 /lambda put dup 88 /X put dup 120 /x put readonly def /FontBBox{0 -250 1171 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR7 %!PS-AdobeFont-1.1: CMR7 1.0 %%CreationDate: 1991 Aug 20 16:39:21 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR7) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR7 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 49 /one put dup 50 /two put readonly def /FontBBox{-27 -250 1122 750}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: MSBM10 %!PS-AdobeFont-1.1: MSBM10 2.1 %%CreationDate: 1993 Sep 17 11:10:37 % Math Symbol fonts were designed by the American Mathematical Society. % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 80 /P put dup 82 /R put readonly def /FontBBox{-55 -420 2343 920}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMSY10 %!PS-AdobeFont-1.1: CMSY10 1.0 %%CreationDate: 1991 Aug 15 07:20:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMSY10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /minus put dup 6 /plusminus put dup 20 /lessequal put dup 24 /similar put dup 25 /approxequal put dup 33 /arrowright put dup 50 /element put dup 70 /F put dup 102 /braceleft put dup 103 /braceright put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMR10 %!PS-AdobeFont-1.1: CMR10 1.00B %%CreationDate: 1992 Feb 19 19:54:52 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.00B) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMR10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 10 /Omega put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 52 /four put dup 53 /five put dup 54 /six put dup 55 /seven put dup 57 /nine put dup 58 /colon put dup 61 /equal put dup 91 /bracketleft put dup 93 /bracketright put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec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130A811DEA77D218A56B0F3E4DB66DE00E12063AC9FE867776B4F9B1B4041627 6701329FF156377C4951AB231CF0FFFB97B302D2AFE07F1FC1B101B745FDB323 E73D55732917428DB958A8A11935D403A04371904C4222747118BE52E20AF561 8D83EDB9D01956FC674DDFBCB00079492B50F8B74EDFF50DC2811B0062ED001C C62C96468DE6AC495E8CF3BCD6CD5B5243587E111771DB5B50EE3790EC1F5080 1DEDE25D89AEE4A134637919839C5DDC6609788EC020E01CD947CE5261C622E9 B0E9B49F9DD57341BB53A55DB6D86E493418CE5ECCCB0AC00D1AE1BF07EF52C3 B673C995AC3115559E8610862759AAC244483B46C9E1956DD8004C0AD7E0DA46 1DA44F17933BDE895B160FFF45A053B4B01835AD589159B3E7E6CE5E687A4933 92408077BF689EEA54E039AC6911F7E76DC09BE0E523A3713E67E7AD3A51D87F E07CDD51D5538BA2060BE6E1288156373897D55E3F1E2C90809109221B2C5537 A1EA764C6C2EBE09B365B8BE19AD474D03725EF1F2E7F83F1988264DEA335560 DE8F0C9175EB3E8659A0FE54F834FDBB265EC1F73D05D71E145DACDA5CD9E8FA 061CB351BDF602D569FAE8FAA71906B65E4C05FFFAD88BF646EF9909F872989B F2495EEF1A6A10EAC65AEE9F2CC821F66FA0B586258F5B203B68DA69AD947580 A9A0C73A3F948198DD4807CBC40F7DC49AEE39825CEB1793DB29945BCCD361EA C57EA564539B0492BBCA324DB85FC324C3DE28D98D964FCE8FD2FF9AC6610FCB FF0CF86BE06E79C724BFE081246373B500C6E0903B3A7A6FFB080A 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 0000000000000000000000000000000000000000000000000000000000000000 cleartomark %%EndFont %%BeginFont: CMMI10 %!PS-AdobeFont-1.1: CMMI10 1.100 %%CreationDate: 1996 Jul 23 07:53:57 % Copyright (C) 1997 American Mathematical Society. All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.100) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (CMMI10) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 21 /lambda put dup 33 /omega put dup 58 /period put dup 59 /comma put dup 60 /less put dup 62 /greater put dup 67 /C put dup 70 /F put dup 78 /N put dup 80 /P put dup 88 /X put dup 89 /Y put dup 99 /c put dup 101 /e put dup 102 /f put dup 110 /n put dup 112 /p put dup 120 /x put readonly def /FontBBox{-32 -250 1048 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 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2206 y(\(a\))42 b(Ein)30 b(W\374rfel)h(wird)f(viermal)f(gew)n(orfen.)f (Die)j(Zufallsv)-5 b(ariable)29 b Fi(X)2286 2218 y Fe(1)2353 2206 y Fm(geb)r(e)h(an,)g(wie)g(oft)g(die)g(Augenzahl)g(ec)n(h)n(t)208 2306 y(kleiner)20 b(als)h(3)g(ist.)h(Geb)r(en)f(Sie)h(eine)f(geeignete) g(Darstellung)f(v)n(on)h Fi(X)2346 2318 y Fe(1)2406 2306 y Fh(:)i(\012)g Fg(!)g Fi(C)28 b Fm(mit)22 b(einem)f(en)n(tsprec)n (henden)208 2406 y(Grundraum)32 b Fh(\012)h Fm(und)g(W)-7 b(erteb)r(ereic)n(h)33 b Fi(C)39 b Fm(an.)33 b(Bestimmen)g(und)g (skizzieren)f(Sie)h(die)h(V)-7 b(erteilungsfunktion)208 2505 y(v)n(on)26 b Fi(X)433 2517 y Fe(1)470 2505 y Fm(.)i(Berec)n(hnen) f(Sie)g(die)h(W)-7 b(ahrsc)n(heinlic)n(hk)n(eit)26 b Fi(P)12 b Fh(\()p Fi(X)2063 2517 y Fe(1)2124 2505 y Fi(>)22 b Fh(2\))p Fm(.)55 2655 y(\(b\))43 b(Sei)27 b Fi(p)c Fg(2)h Fh([0)p Fi(;)14 b Fh(1])p Fm(.)26 b(Die)i(Zufallsv)-5 b(ariable)26 b Fi(X)1475 2667 y Fe(2)1540 2655 y Fm(hab)r(e)i(die)f(V) -7 b(erteilungsfunktion)1181 2984 y Fi(F)1234 2996 y Fd(X)1288 3004 y Fc(2)1325 2984 y Fh(\()p Fi(x)p Fh(\))24 b(=)1548 2764 y Fb(8)1548 2839 y(>)1548 2864 y(>)1548 2889 y(<)1548 3038 y(>)1548 3063 y(>)1548 3088 y(:)1663 2834 y Fh(0)p Fi(;)469 b(x)24 b(<)f Fg(\000)p Fh(1)p Fi(;)1663 2933 y Fh(1)18 b Fg(\000)g Fi(p;)326 b Fg(\000)p Fh(1)23 b Fg(\024)f Fi(x)i(<)e Fh(0)p Fi(;)1663 3033 y Fh(1)c Fg(\000)g Fi(p)g Fh(+)1959 3000 y Fe(1)p 1959 3014 34 4 v 1959 3062 a(2)2002 3033 y Fi(xp;)83 b Fh(0)23 b Fg(\024)g Fi(x)g Fg(\024)g Fh(2)p Fi(;)1663 3133 y Fh(1)p Fi(;)469 b(x)24 b(>)f Fh(2)208 3313 y Fm(Skizzieren)i(Sie)h(die) g(V)-7 b(erteilungsfunktion)26 b Fi(F)1650 3325 y Fd(X)1704 3333 y Fc(2)1768 3313 y Fm(und)h(b)r(erec)n(hnen)e(Sie)i Fi(P)12 b Fh(\()p Fg(\000)p Fh(1)22 b Fi(<)g(X)2838 3325 y Fe(2)2899 3313 y Fg(\024)g Fh(1\))p Fm(,)k Fi(P)12 b Fh(\()p Fi(X)3275 3325 y Fe(2)3335 3313 y Fh(=)23 b(0\))j Fm(und)208 3413 y Fi(P)12 b Fh(\()p Fi(X)374 3425 y Fe(2)434 3413 y Fh(=)22 b Fg(\000)p Fh(1\))p Fm(.)0 3563 y Fj(Aufgab)s(e)32 b(3)145 b Fm(\(2)28 b(+)f(2)g(+)g(3)g(Punkte\))0 3686 y(Sei)f Fh(\(\012)p Fi(;)14 b Fg(F)8 b Fi(;)14 b(P)e Fh(\))26 b Fm(eine)g(b)r(eliebiger)f(W)-7 b(ahrsc)n(heinlic)n(hk)n (eitsraum,)23 b(und)k(die)f(F)-7 b(unktion)26 b Fi(f)31 b Fh(:)23 b Ff(R)g Fg(!)h Ff(R)h Fm(sei)h(gegeb)r(en)f(durc)n(h)1038 3916 y Fi(f)9 b Fh(\()p Fi(x)p Fh(\))23 b(=)1310 3799 y Fb(\032)1414 3865 y Fi(c)14 b(e)1503 3835 y Fa(\000)p Fd(\025x)1635 3865 y Fh(\(1)19 b Fg(\000)f Fi(e)1850 3835 y Fa(\000)p Fd(\025x)1982 3865 y Fh(\))97 b Fi(;)14 b Fm(falls)42 b Fi(x)23 b(>)g Fh(0)14 b Fi(;)1693 3965 y Fh(0)376 b Fi(;)14 b Fm(falls)42 b Fi(x)23 b Fg(\024)g Fh(0)14 b Fi(;)0 4141 y Fm(w)n(ob)r(ei)27 b Fi(c)c Fg(2)h Ff(R)j Fm(und)h Fi(\025)c(>)e Fh(0)p Fm(.)60 4291 y(\(a\))42 b(F\374r)27 b(w)n(elc)n(hes)g Fi(c)c Fg(2)g Ff(R)28 b Fm(ist)f Fi(f)37 b Fm(eine)27 b(Dic)n(h)n(te?)55 4440 y(\(b\))43 b(Bestimmen)27 b(Sie)h(die)g(zu)f Fi(f)37 b Fm(geh\366rige)25 b(V)-7 b(erteilungsfunktion.)65 4589 y(\(c\))42 b(Sei)23 b Fi(X)30 b Fm(eine)24 b(absolutstetige)e(Zufallsv) -5 b(ariable)22 b(mit)j(Dic)n(h)n(te)e Fi(f)9 b Fm(.)23 b(Berec)n(hnen)g(Sie)h Fi(P)12 b Fh(\(1)22 b Fg(\024)h Fi(X)29 b Fg(\024)23 b Fh(4\))g Fm(und)h(skizzie-)208 4689 y(ren)i(Sie)h Fi(f)35 b Fm(f\374r)27 b Fi(\025)c Fh(=)g(1)p Fm(.)j(F\374gen)h(Sie)g(in)f(der)h(Skizze)f(eine)h(ansc)n (haulic)n(he)e(In)n(terpretation)g(v)n(on)h Fi(P)12 b Fh(\(1)23 b Fg(\024)g Fi(X)29 b Fg(\024)23 b Fh(4\))208 4789 y Fm(und)28 b(die)f(V)-7 b(erteilungsfunktion)28 b(hinzu.)0 5038 y Fj(Aufgab)s(e)k(4)145 b Fm(\(6)28 b(Punkte\))0 5161 y(Ein)36 b(Mein)n(ungsforsc)n(h)n(ungsinstitut)e(will)i(den)f(v)n (oraussic)n(h)n(tlic)n(hen)e(Stimmenan)n(teil)j Fi(p)f Fm(der)g(P)n(artei)g(A)h(ermitteln,)0 5261 y(w)n(enn)h(am)f(Sonn)n(tag) g(Bundestagsw)n(ahl)f(w)n(\344re.)h(Dazu)h(w)n(erden)f Fi(n)g Fm(W)-7 b(ahlb)r(erec)n(h)n(tigte)37 b(b)r(efragt)f(und)h(jew)n (eils)g(v)n(er-)0 5360 y(merkt,)e(ob)h(sie)f(f\374r)g(die)h(P)n(artei)f (A)h(stimmen)g(w)n(erden)f(o)r(der)g(nic)n(h)n(t.)g(Wieviele)h(W)-7 b(ahlb)r(erec)n(h)n(tigte)34 b(m)n(\374ssen)h(min-)0 5460 y(destens)d(b)r(efragt)f(w)n(erden,)g(um)i(den)f(Stimmenan)n(teil) g(der)f(P)n(artei)h(mit)g(einer)g(Sic)n(herheit)f(v)n(on)g(mindestens)h (95\045)0 5559 y(auf)j(eine)g(absolute)f(Genauigk)n(eit)f(v)n(on)h Fg(\006)p Fm(2\045)g(v)n(orhersagen)e(zu)j(k)n(\366nnen?)f(\(Hin)n(w)n (eis)g(:)h(Zeigen)f(Sie)h(zuerst,)f(dass)0 5659 y Fi(F)53 5671 y Fd(X)117 5659 y Fh(\()p Fg(\000)p Fi(x)p Fh(\))42 b(=)g(1)25 b Fg(\000)h Fi(F)653 5671 y Fd(X)716 5659 y Fh(\()p Fi(x)p Fh(\))40 b Fm(f\374r)f Fi(X)48 b Fg(\030)42 b Fi(N)9 b Fh(\(0)p Fi(;)14 b Fh(1\))p Fm(.)38 b(Ben)n(utzen)h(Sie)g (dann)g(den)g(zen)n(tralen)f(Grenzw)n(ertsatz)f(v)n(on)h(De)0 5759 y(Moivre-Laplace)25 b(und)j Fi(F)806 5771 y Fd(X)870 5759 y Fh(\(1)p Fi(:)p Fh(96\))22 b Fg(\031)g Fh(0)p Fi(:)p Fh(975)p Fm(.\))p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF