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% Copyright (C) 1997 American Mathematical Society. All Rights Reserved.
11 dict begin
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/FontMatrix [0.001 0 0 0.001 0 0] readonly def
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currentdict end
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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
dup 61 /equal put
readonly def
/FontBBox{-27 -250 1122 750}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 1 /periodcentered put
dup 15 /bullet put
dup 21 /greaterequal put
dup 40 /arrowdblleft put
dup 41 /arrowdblright put
dup 50 /element put
dup 59 /emptyset put
dup 70 /F put
dup 91 /union put
dup 92 /intersection put
dup 102 /braceleft put
dup 103 /braceright put
dup 106 /bar put
readonly def
/FontBBox{-29 -960 1116 775}readonly def
currentdict end
currentfile eexec
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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 58 /period put
dup 59 /comma put
dup 60 /less put
dup 61 /slash put
dup 65 /A put
dup 66 /B put
dup 67 /C put
dup 68 /D put
dup 80 /P put
dup 88 /X put
dup 89 /Y put
dup 99 /c put
dup 105 /i put
dup 110 /n put
dup 112 /p put
dup 113 /q put
readonly def
/FontBBox{-32 -250 1048 750}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 48 /zero put
dup 49 /one put
dup 50 /two put
dup 51 /three put
dup 56 /eight put
dup 61 /equal put
dup 73 /I put
dup 78 /N put
dup 105 /i put
dup 109 /m put
dup 110 /n put
readonly def
/FontBBox{-251 -250 1009 969}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: SFBX1000
%!FontType1-1.0: SFBX1000 0.3
%%CreationDate: Wed Sep 12 2001
% Copyright (c) 2001 Vladimir Volovich <vvv@vsu.ru>.
% See the file COPYING (GNU General Public License) for license conditions.
% Converted from METAFONT EC/TC and LH fonts:
% ecbx1000, tcbx1000, labx1000, lbbx1000, lcbx1000, rxbx1000.
11 dict begin
/FontInfo 6 dict dup begin
/version (0.3) def
/FullName (Computer Modern Bold Extended) def
/FamilyName (Computer Modern) def
/ItalicAngle 0 def
/isFixedPitch false def
/Weight (Bold) def
end readonly def
/FontName /SFBX1000 def
/Encoding StandardEncoding def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] def
/FontBBox{-229 -316 1737 939}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: SFRM1440
%!FontType1-1.0: SFRM1440 0.3
%%CreationDate: Wed Sep 12 2001
% Copyright (c) 2001 Vladimir Volovich <vvv@vsu.ru>.
% See the file COPYING (GNU General Public License) for license conditions.
% Converted from METAFONT EC/TC and LH fonts:
% ecrm1440, tcrm1440, larm1440, lbrm1440, lcrm1440, rxrm1440.
11 dict begin
/FontInfo 6 dict dup begin
/version (0.3) def
/FullName (Computer Modern Roman) def
/FamilyName (Computer Modern) def
/ItalicAngle 0 def
/isFixedPitch false def
/Weight (Medium) def
end readonly def
/FontName /SFRM1440 def
/Encoding StandardEncoding def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] def
/FontBBox{-178 -319 1370 944}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: SFBX1440
%!FontType1-1.0: SFBX1440 0.3
%%CreationDate: Wed Sep 12 2001
% Copyright (c) 2001 Vladimir Volovich <vvv@vsu.ru>.
% See the file COPYING (GNU General Public License) for license conditions.
% Converted from METAFONT EC/TC and LH fonts:
% ecbx1440, tcbx1440, labx1440, lbbx1440, lcbx1440, rxbx1440.
11 dict begin
/FontInfo 6 dict dup begin
/version (0.3) def
/FullName (Computer Modern Bold Extended) def
/FamilyName (Computer Modern) def
/ItalicAngle 0 def
/isFixedPitch false def
/Weight (Bold) def
end readonly def
/FontName /SFBX1440 def
/Encoding StandardEncoding def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] def
/FontBBox{-218 -316 1652 915}readonly def
currentdict end
currentfile eexec
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cleartomark
%%EndFont 
%%BeginFont: SFRM1000
%!FontType1-1.0: SFRM1000 0.3
%%CreationDate: Wed Sep 12 2001
% Copyright (c) 2001 Vladimir Volovich <vvv@vsu.ru>.
% See the file COPYING (GNU General Public License) for license conditions.
% Converted from METAFONT EC/TC and LH fonts:
% ecrm1000, tcrm1000, larm1000, lbrm1000, lcrm1000, rxrm1000.
11 dict begin
/FontInfo 6 dict dup begin
/version (0.3) def
/FullName (Computer Modern Roman) def
/FamilyName (Computer Modern) def
/ItalicAngle 0 def
/isFixedPitch false def
/Weight (Medium) def
end readonly def
/FontName /SFRM1000 def
/Encoding StandardEncoding def
/PaintType 0 def
/FontType 1 def
/FontMatrix [0.001 0 0 0.001 0 0] def
/FontBBox{-189 -321 1456 937}readonly def
currentdict end
currentfile eexec
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1401 y Fb(S)374 1422 y Fc(n)374 1488 y(i)p Fd(=1)499
1464 y Ff(A)561 1476 y Fc(i)589 1464 y Fg(\))24 b(=)e(1)c
Fe(\000)875 1401 y Fb(Q)954 1422 y Fc(n)954 1488 y(i)p
Fd(=1)1065 1464 y Fg(\(1)h Fe(\000)f Ff(P)12 b Fg(\()p
Ff(A)1400 1476 y Fc(i)1428 1464 y Fg(\)\))28 b Fk(gilt.)65
1613 y(\(c\))42 b Ff(P)12 b Fg(\()305 1551 y Fb(S)374
1571 y Fa(1)374 1638 y Fc(i)p Fd(=1)499 1613 y Ff(A)561
1625 y Fc(i)589 1613 y Fg(\))24 b(=)e(1)h Fe(\()-14 b(\))23
b Ff(P)12 b Fg(\()p Fk(lim)28 b(sup)1337 1633 y Fc(i)1365
1613 y Ff(A)1427 1625 y Fc(i)1455 1613 y Fg(\))23 b(=)g(1)k
Fk(gilt,)g(falls)h Ff(P)12 b Fg(\()p Ff(A)2170 1625 y
Fc(i)2198 1613 y Fg(\))23 b Ff(<)g Fg(1)k Fk(f\374r)h(jedes)f
Ff(i)c Fe(2)g Fg(I)-19 b(N)q Fk(.)0 1862 y Fh(Aufgab)s(e)32
b(2)145 b Fk(\(2)28 b(+)f(2)g(Punkte\))60 2012 y(\(a\))42
b(Das)22 b(Ereignis)h Ff(A)g Fk(sei)g(unabh\344ngig)f(v)n(on)h(den)g
(Ereignissen)f Ff(B)2127 2024 y Fd(1)2188 2012 y Fk(und)h
Ff(B)2412 2024 y Fd(2)2449 2012 y Fk(.)h(W)-7 b(eiter)23
b(gelte)g Ff(B)3016 2024 y Fd(1)3063 2012 y Fe(\\)10
b Ff(B)3191 2024 y Fd(2)3251 2012 y Fg(=)22 b Fe(;)p
Fk(.)h(Zeigen)208 2111 y(Sie,)k(dass)g Ff(A)h Fk(und)g
Ff(B)864 2123 y Fd(1)920 2111 y Fe([)18 b Ff(B)1056 2123
y Fd(2)1121 2111 y Fk(unabh\344ngig)27 b(sind.)55 2261
y(\(b\))43 b(Die)31 b(Ereignisse)f Ff(A)h Fk(und)g Ff(B)k
Fk(seien)c(unabh\344ngig)e(und)i(es)g(gelte)f Ff(P)12
b Fg(\()p Ff(A)p Fg(\))29 b(=)f(1)p Ff(=)p Fg(2)p Fk(,)i
Ff(P)12 b Fg(\()p Ff(B)t Fg(\))29 b(=)f(1)p Ff(=)p Fg(3)p
Fk(.)h(Mit)j(w)n(elc)n(her)208 2360 y(W)-7 b(ahrsc)n(heinlic)n(hk)n
(eit)26 b(tritt)j(mindestens)f(eines)f(dieser)h(Ereignisse)f(ein?)h
(Mit)g(w)n(elc)n(her)f(W)-7 b(ahrsc)n(heinlic)n(hk)n(eit)208
2460 y(tritt)28 b(genau)e(eines)i(dieser)f(Ereignisse)f(ein?)0
2709 y Fh(Aufgab)s(e)32 b(3)145 b Fk(\(1)28 b(+)f(1)g(+)g(1)g(+)h(1)f
(Punkte\))0 2856 y(Es)h(w)n(erden)f(nac)n(heinander)f(zw)n(ei)h
(M\374nzen)h(gew)n(orfen.)e(Die)i(Ereignisse)f Ff(A)p
Fk(,)h Ff(B)t Fk(,)g Ff(C)33 b Fk(und)28 b Ff(D)i Fk(seien)e(gegeb)r
(en)e(durc)n(h)125 3005 y Fe(\017)41 b Ff(A)27 b Fk(:)h(die)g(zuerst)f
(gew)n(orfene)f(M\374nze)i(zeigt)f(K)n(opf)125 3155 y
Fe(\017)41 b Ff(B)31 b Fk(:)d(es)f(ersc)n(hein)n(t)g(mindestens)h
(einmal)f(K)n(opf)125 3304 y Fe(\017)41 b Ff(C)33 b Fk(:)28
b(es)g(ersc)n(hein)n(t)e(mindestens)i(einmal)f(Zahl)125
3454 y Fe(\017)41 b Ff(D)29 b Fk(:)f(die)g(zw)n(eite)f(M\374nze)h
(zeigt)f(K)n(opf)0 3603 y(\334b)r(erpr\374fen)h(Sie,)g(ob)f(folgende)g
(Ereignisse)g(unabh\344ngig)f(sind)i(\(mit)g(Begr\374ndung\):)0
3703 y(\(a\))g Ff(A)g Fk(und)g Ff(C)6 b Fk(;)28 b(\(b\))g
Ff(A)g Fk(und)g Ff(D)r Fk(;)g(\(c\))g Ff(B)k Fk(und)c
Ff(C)6 b Fk(;)28 b(\(d\))g Ff(B)k Fk(und)c Ff(D)0 3952
y Fh(Aufgab)s(e)k(4)145 b Fk(\(3)28 b(+)f(3)g(Punkte\))0
4099 y(Sei)40 b Fg(\(\012)p Ff(;)14 b Fe(F)8 b Ff(;)14
b(P)e Fg(\))41 b Fk(ein)f(W)-7 b(ahrsc)n(heinlic)n(hk)n(eitsraum)38
b(und)j Ff(A;)14 b(B)48 b Fe(2)d(F)8 b Fk(.)40 b(Bew)n(eisen)g(o)r(der)
f(widerlegen)h(Sie)g(folgende)0 4198 y(Aussagen:)60 4348
y(\(a\))i(Es)27 b(sei)h Fg(0)22 b Ff(<)h(P)12 b Fg(\()p
Ff(A)p Fg(\))24 b Ff(<)e Fg(1)p Fk(.)28 b(Dann)f(gilt)1010
4530 y Ff(P)12 b Fg(\()p Ff(A)19 b Fe(\\)g Ff(B)t Fg(\))k(=)g
Ff(P)12 b Fg(\()p Ff(A)p Fg(\))p Ff(P)g Fg(\()p Ff(B)t
Fg(\))24 b Fe(\()-14 b(\))23 b Ff(P)12 b Fg(\()p Ff(B)28
b Fe(j)23 b Ff(A)p Fg(\))g(=)g Ff(P)12 b Fg(\()p Ff(B)27
b Fe(j)d Ff(A)2793 4496 y Fc(c)2827 4530 y Fg(\))55 4763
y Fk(\(b\))43 b(Es)27 b(gibt)h(Ereignisse)f Ff(A)h Fk(und)g
Ff(B)j Fk(mit)851 4945 y Fg(0)23 b Ff(<)f(P)12 b Fg(\()p
Ff(B)t Fg(\))24 b Ff(<)f Fg(1)p Ff(;)14 b(P)e Fg(\()p
Ff(A)22 b Fe(j)i Ff(B)t Fg(\))f(=)g Ff(P)12 b Fg(\()p
Ff(A)p Fg(\))24 b Fk(und)g Ff(P)12 b Fg(\()p Ff(A)19
b Fe([)g Ff(B)t Fg(\))k(=)g Ff(P)12 b Fg(\()p Ff(A)19
b Fe(\\)f Ff(B)t Fg(\))0 5178 y Fh(Aufgab)s(e)32 b(5)145
b Fk(\(2)28 b(+)f(1)g(+)g(1)g(Punkte\))0 5325 y(Sei)h
Ff(X)34 b Fk(eine)27 b(Zufallsv)-5 b(ariable)26 b(mit)j
Ff(p)1156 5337 y Fc(i)1206 5325 y Fg(=)23 b Ff(P)12 b
Fg(\()p Ff(X)29 b Fg(=)23 b Ff(i)p Fg(\))g(=)f Ff(c)d
Fe(\001)f Ff(q)1884 5295 y Fc(i)1940 5325 y Fk(f\374r)27
b Ff(i)c Fg(=)f(1)p Ff(;)14 b Fg(2)p Ff(;)g(:)g(:)g(:)27
b Fk(,)h Ff(c)23 b Fe(\025)f Fg(0)27 b Fk(und)h Fg(0)23
b Ff(<)g(q)j(<)c Fg(1)p Fk(.)60 5474 y(\(a\))42 b(Bestimmen)27
b(Sie)h Ff(c)p Fk(,)g(so)f(dass)f Fe(f)p Ff(p)1227 5486
y Fc(i)1254 5474 y Fe(g)h Fk(eine)h(Z\344hldic)n(h)n(te)f(\(=)g(W)-7
b(ahrsc)n(heinlic)n(hk)n(eitsfunktion\))27 b(bildet.)55
5624 y(\(b\))43 b(Bestimmen)27 b(Sie)h Ff(P)12 b Fg(\()p
Ff(X)30 b Fk(ist)e(gerade)n Fg(\))p Fk(.)65 5773 y(\(c\))42
b(Bestimmen)27 b(Sie)h(die)g(Z\344hldic)n(h)n(te)f(der)g(Zufallsv)-5
b(ariablen)26 b Ff(Y)42 b Fg(=)22 b(min)q Fe(f)p Ff(X)r(;)14
b Fg(8)p Fe(g)p Fk(.)p eop end
%%Trailer

userdict /end-hook known{end-hook}if
%%EOF