%!PS-Adobe-2.0 %%Creator: dvips(k) 5.96dev Copyright 2007 Radical Eye Software %%Title: blatt12.dvi %%CreationDate: Thu Jan 15 17:04:22 2009 %%Pages: 1 %%PageOrder: Ascend %%BoundingBox: 0 0 595 842 %%DocumentFonts: SFRM1000 SFBX1440 SFRM1440 SFBX1000 CMMI10 CMSY10 CMR10 %%+ CMMI7 CMR7 CMR5 CMMI5 MSBM10 %%DocumentPaperSizes: a4 %%EndComments %DVIPSWebPage: (www.radicaleye.com) %DVIPSCommandLine: dvips -D600 blatt12.dvi %DVIPSParameters: dpi=600 %DVIPSSource: TeX output 2009.01.15:1427 %%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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All Rights Reserved) readonly def /FullName (CMMI5) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI5 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 110 /n put readonly def /FontBBox{37 -250 1349 750}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 49 /one put dup 50 /two put readonly def /FontBBox{-341 -250 1304 965}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 43 /plus put dup 48 /zero put dup 49 /one put dup 50 /two put dup 80 /P put dup 91 /bracketleft put dup 93 /bracketright put readonly def /FontBBox{-27 -250 1122 750}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 58 /period put dup 59 /comma put dup 61 /slash put dup 76 /L put dup 80 /P put dup 88 /X put dup 100 /d put dup 102 /f put dup 110 /n put dup 115 /s put readonly def /FontBBox{0 -250 1171 750}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA0529731C99A784CCBE85B4993B2EEBDE 3B12D472B7CF54651EF21185116A69AB1096ED4BAD2F646635E019B6417CC77B 532F85D811C70D1429A19A5307EF63EB5C5E02C89FC6C20F6D9D89E7D91FE470 B72BEFDA23F5DF76BE05AF4CE93137A219ED8A04A9D7D6FDF37E6B7FCDE0D90B 986423E5960A5D9FBB4C956556E8DF90CBFAEC476FA36FD9A5C8175C9AF513FE D919C2DDD26BDC0D99398B9F4D03D77639DF1232A4D6233A9CAF69B151DFD33F C0962EAC6E3EBFB8AD256A3C654EAAF9A50C51BC6FA90B61B60401C235AFAB7B B078D20B4B8A6D7F0300CF694E6956FF9C29C84FCC5C9E8890AA56B1BC60E868 DA8488AC4435E6B5CE34EA88E904D5C978514D7E476BF8971D419363125D4811 4D886EDDDCDDA8A6B0FDA5CF0603EA9FA5D4393BEBB26E1AB11C2D74FFA6FEE3 FAFBC6F05B801C1C3276B11080F5023902B56593F3F6B1F37997038F36B9E3AB 76C2E97E1F492D27A8E99F3E947A47166D0D0D063E4E6A9B535DC9F1BED129C5 123775D5D68787A58C93009FD5DA55B19511B95168C83429BD2D878207C39770 012318EA7AA39900C97B9D3859E3D0B04750B8390BF1F1BC29DC22BCAD50ECC6 A3C633D0937A59E859E5185AF9F56704708D5F1C50F78F43DFAC43C4E7DC9413 44CEFE43279AFD3C167C942889A352F2FF806C2FF8B3EB4908D50778AA58CFFC 4D1B14597A06A994ED8414BBE8B26E74D49F6CF54176B7297CDA112A69518050 01337CBA5478EB984CDD22020DAED9CA8311C33FBCC84177F5CE870E709FC608 D28B3A7208EFF72988C136142CE79B4E9C7B3FE588E9824ABC6F04D141E589B3 914A73A42801305439862414F893D5B6C327A7EE2730DEDE6A1597B09C258F05 261BC634F64C9F8477CD51634BA648FC70F659C90DC042C0D6B68CD1DF36D615 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%!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 58 /colon put dup 61 /equal put dup 63 /question put dup 69 /E put dup 73 /I put dup 91 /bracketleft put dup 93 /bracketright put dup 97 /a put dup 105 /i put dup 109 /m put dup 110 /n put dup 112 /p put dup 120 /x put readonly def /FontBBox{-251 -250 1009 969}readonly def currentdict end currentfile eexec D9D66F633B846A97B686A97E45A3D0AA052A014267B7904EB3C0D3BD0B83D891 016CA6CA4B712ADEB258FAAB9A130EE605E61F77FC1B738ABC7C51CD46EF8171 9098D5FEE67660E69A7AB91B58F29A4D79E57022F783EB0FBBB6D4F4EC35014F 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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (1.0) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. 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Fl(-v)n(erteilten)28 b(Zufallsv)-5 b(ariablen)28 b(und)208 3029 y Fh(Y)256 3041 y Fe(n)324 3029 y Ff(=)23 b Fh(n)18 b Fg(\001)g Ff(min)q Fg(f)p Fh(X)771 3041 y Fd(1)807 3029 y Fh(;)c(:)g(:)g(:)g(;)g (X)1061 3041 y Fe(n)1106 3029 y Fg(g)27 b Fl(gilt)h Fh(Y)1371 3041 y Fe(n)1489 2982 y(d)1439 3029 y Fg(\000)-14 b(!)23 b Fh(Z)33 b Fl(mit)28 b Fh(Z)h Fg(\030)23 b Fh(E)5 b(xp)p Ff(\(1\))p Fl(.)65 3179 y(\(c\))42 b(Sei)27 b Fg(f)p Fh(Y)431 3191 y Fe(n)476 3179 y Fg(g)h Fl(eine)g(F)-7 b(olge)27 b(v)n(on)g(unabh\344ngigen)f(und)i(iden)n(tisc)n(h)g(v)n (erteilten)f(Zufallsv)-5 b(ariablen)27 b(mit)h Fa(E)p Fg(j)p Fh(Y)3383 3191 y Fd(1)3421 3179 y Fg(j)23 b Fh(<)g Fg(1)p Fl(,)208 3278 y(und)c(sei)g Fh(X)546 3290 y Fe(n)614 3278 y Ff(=)716 3246 y Fd(1)p 712 3260 V 712 3307 a Fe(n)763 3278 y Fh(Y)811 3290 y Fe(n)875 3278 y Fl(f\374r)h(jedes)f Fh(n)k Fg(2)g Fa(N)p Fl(.)c(Zeigen)g(Sie,)g(dass)f(die)i(F)-7 b(olge)18 b Fg(f)p Fh(X)2470 3290 y Fe(n)2515 3278 y Fg(g)g Fl(fast)h(sic)n(her)g(gegen)f(0)g(k)n(on)n(v)n(ergiert.)0 3516 y Fi(Aufgab)s(e)32 b(3)145 b Fl(\(2)28 b(+)f(2)g(+)g(2)g(Punkte\)) 0 3639 y(Zeigen)g(Sie)h(folgende)f(Aussagen:)60 3741 y(\(a\))42 b(F\374r)32 b(die)h(F)-7 b(olge)32 b Fg(f)p Fh(X)846 3753 y Fe(n)890 3741 y Fg(g)h Fl(v)n(on)f(unabh\344ngigen,)f (iden)n(tisc)n(h)h Fh(U)9 b Ff(\(0)p Fh(;)14 b(\022)r Ff(\))p Fl(-v)n(erteilten)32 b(Zufallsv)-5 b(ariablen)32 b(mit)h Fh(\022)h(>)d Ff(0)208 3865 y Fl(gilt)c Ff(max)p Fg(f)p Fh(X)621 3877 y Fd(1)657 3865 y Fh(;)14 b(:)g(:)g(:)g(;)g(X)911 3877 y Fe(n)956 3865 y Fg(g)1061 3818 y Fe(P)1020 3865 y Fg(\000)-14 b(!)37 b Fh(\022)r Fl(.)55 4015 y(\(b\))43 b(Sei)34 b Fg(f)p Fh(X)459 4027 y Fe(n)504 4015 y Fg(g)g Fl(eine)h(monoton)e(w)n(ac)n(hsende)h(F)-7 b(olge)34 b(v)n(on)f(Zufallsv)-5 b(ariablen.)34 b(Zeigen)f(Sie,)i(dass)f(die)h(F) -7 b(olge)34 b(fast)208 4139 y(sic)n(her)26 b(gegen)h(eine)g(Zufallsv) -5 b(ariable)26 b Fh(X)34 b Fl(k)n(on)n(v)n(ergiert,)25 b(falls)i Fh(X)2196 4151 y Fe(n)2284 4092 y Fd(P)2264 4139 y Fg(!)c Fh(X)34 b Fl(gilt.)65 4288 y(\(c\))42 b(Zeigen)26 b(Sie,)i(dass)f(die)h(F)-7 b(olge)27 b(in)g(\(a\))h(auc)n(h)f(fast)h (sic)n(her)e(und)i(im)g Fh(L)2322 4258 y Fd(1)2386 4288 y Fl(gegen)f Fh(\022)j Fl(k)n(on)n(v)n(ergiert.)0 4525 y Fi(Aufgab)s(e)i(4)145 b Fl(\(6)28 b(Punkte\))0 4649 y(Sei)g Fh(')23 b Ff(:)g Fa(R)g Fg(7\000)-14 b(!)23 b Fa(R)28 b Fl(stetig)f(und)h Fh(X)r(;)14 b(X)1154 4661 y Fe(n)1199 4649 y Fh(;)g(Y)5 b(;)14 b(Y)1374 4661 y Fe(n)1442 4649 y Ff(:)23 b(\012)g Fg(\000)-14 b(!)23 b Fa(R)k Fl(b)r(eliebige)h(Zufallsv)-5 b(ariablen)26 b(auf)i Ff(\(\012)p Fh(;)14 b Fg(F)8 b Fh(;)14 b(P)e Ff(\))p Fl(,)27 b(dann)h(gilt:)101 4792 y(1.)42 b Fh(X)277 4804 y Fe(n)322 4792 y Fh(Y)370 4804 y Fe(n)452 4741 y(f)s(:s:)438 4792 y Fg(\000)-14 b(!)23 b Fh(X)7 b(Y)18 b Fl(,)27 b(falls)h Fh(X)1030 4804 y Fe(n)1112 4741 y(f)s(:s:)1098 4792 y Fg(\000)-14 b(!)23 b Fh(X)34 b Fl(und)28 b Fh(Y)1572 4804 y Fe(n)1654 4741 y(f)s(:s:)1640 4792 y Fg(\000)-14 b(!)23 b Fh(Y)c Fl(,)101 4961 y(2.)42 b Fh(X)277 4973 y Fe(n)322 4961 y Fh(Y)370 4973 y Fe(n)479 4914 y(P)438 4961 y Fg(\000)-14 b(!)23 b Fh(X)7 b(Y)18 b Fl(,)27 b(falls)h Fh(X)1030 4973 y Fe(n)1139 4914 y(P)1098 4961 y Fg(\000)-14 b(!)23 b Fh(X)34 b Fl(und)28 b Fh(Y)1572 4973 y Fe(n)1681 4914 y(P)1640 4961 y Fg(\000)-14 b(!)23 b Fh(Y)c Fl(,)101 5142 y(3.)42 b Fh(X)277 5154 y Fe(n)322 5142 y Fh(Y)370 5154 y Fe(n)466 5095 y(L)512 5070 y Fc(1)438 5142 y Fg(\000)-14 b(!)23 b Fh(X)7 b(Y)18 b Fl(,)27 b(falls)h Fh(X)1030 5154 y Fe(n)1126 5095 y(L)1172 5070 y Fc(2)1098 5142 y Fg(\000)-14 b(!)23 b Fh(X)34 b Fl(und)28 b Fh(Y)1572 5154 y Fe(n)1668 5095 y(L)1714 5070 y Fc(2)1640 5142 y Fg(\000)-14 b(!)23 b Fh(Y)c Fl(.)101 5316 y(4.)42 b Fh(')p Ff(\()p Fh(X)363 5328 y Fe(n)408 5316 y Ff(\))477 5265 y Fe(f)s(:s:)463 5316 y Fg(\000)-14 b(!)23 b Fh(')p Ff(\()p Fh(X)7 b Ff(\))p Fl(,)28 b(falls)g Fh(X)1108 5328 y Fe(n)1189 5265 y(f)s(:s:)1176 5316 y Fg(\000)-15 b(!)23 b Fh(X)7 b Fl(,)101 5490 y(5.)42 b Fh(')p Ff(\()p Fh(X)363 5502 y Fe(n)408 5490 y Ff(\))505 5443 y Fe(P)463 5490 y Fg(\000)-14 b(!)23 b Fh(')p Ff(\()p Fh(X)7 b Ff(\))p Fl(,)28 b(falls)g Fh(X)1108 5502 y Fe(n)1217 5443 y(P)1176 5490 y Fg(\000)-15 b(!)23 b Fh(X)7 b Fl(,)101 5665 y(6.)42 b Fh(')p Ff(\()p Fh(X)363 5677 y Fe(n)408 5665 y Ff(\))513 5618 y Fe(d)463 5665 y Fg(\000)-14 b(!)23 b Fh(')p Ff(\()p Fh(X)7 b Ff(\))p Fl(,)28 b(falls)g Fh(X)1108 5677 y Fe(n)1225 5618 y(d)1176 5665 y Fg(\000)-15 b(!)23 b Fh(X)7 b Fl(.)p eop end %%Trailer userdict /end-hook known{end-hook}if %%EOF