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cleartomark
%%EndFont 
%%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
dup 33 /arrowright put
dup 49 /infinity put
dup 112 /radical put
readonly def
/FontBBox{-15 -951 1252 782}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 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 20 /lessequal put
dup 24 /similar put
dup 25 /approxequal put
dup 33 /arrowright put
dup 50 /element put
dup 112 /radical put
readonly def
/FontBBox{-29 -960 1116 775}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 25 /pi put
dup 61 /slash put
dup 85 /U put
dup 105 /i put
dup 110 /n put
dup 114 /r put
dup 121 /y put
dup 122 /z 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
dup 53 /five 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: 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 22 /mu put
dup 25 /pi put
dup 27 /sigma put
dup 31 /chi put
dup 58 /period put
dup 59 /comma put
dup 62 /greater put
dup 69 /E put
dup 78 /N put
dup 80 /P put
dup 83 /S put
dup 85 /U put
dup 88 /X put
dup 89 /Y put
dup 98 /b put
dup 100 /d put
dup 101 /e put
dup 110 /n put
dup 112 /p put
dup 114 /r put
dup 120 /x put
dup 121 /y put
dup 122 /z 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 0 /Gamma put
dup 8 /Phi put
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 51 /three put
dup 52 /four put
dup 53 /five put
dup 54 /six put
dup 55 /seven put
dup 56 /eight put
dup 57 /nine put
dup 58 /colon put
dup 61 /equal put
dup 105 /i put
dup 108 /l put
dup 109 /m 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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TeXDict begin 1 0 bop 0 36 a Fn(Prof.)28 b(Dr.)f(V)-7
b(olk)n(er)27 b(Sc)n(hmidt)2303 b(WS)28 b(2008/09)0 135
y(Dipl.-Math.)g(o)r(ec.)f(Ralf)h(Thiedmann)2151 b(5.2.2009)0
235 y(Dipl.-Math.)28 b(o)r(ec.)f(Florian)g(V)-7 b(oss)259
602 y Fm(Elemen)l(tare)44 b(W)-11 b(ahrsc)l(heinlic)l(hk)l(eitsrec)l
(hn)l(ung)45 b(und)e(Statistik)1446 740 y Fl(\334bungsblatt)c(15)746
887 y Fn(\(k)n(eine)28 b(Abgab)r(e;)f(Besprec)n(h)n(ung)f(am)h
(12.2.2009)d(in)k(den)g(\334bungen\))0 1202 y Fk(Aufgab)s(e)k(1)145
b Fn(\(5)28 b(Punkte\))0 1325 y(Sei)i Fj(\()p Fi(X)237
1337 y Fh(1)274 1325 y Fi(;)14 b(:)g(:)g(:)g(;)g(X)528
1337 y Fg(n)573 1325 y Fj(\))30 b Fn(eine)g(Zufallsstic)n(hprob)r(e)f
(mit)h Fi(X)1678 1337 y Fh(1)1742 1325 y Ff(\030)d Fi(E)5
b(xp)p Fj(\()p Fi(\025)p Fj(\))p Fn(,)31 b(d.h.)f(insb)r(esondere,)f
(dass)g Fi(X)3088 1337 y Fh(1)3125 1325 y Fi(;)14 b(:)g(:)g(:)g(;)g(X)
3379 1337 y Fg(n)3454 1325 y Fn(unab-)0 1425 y(h\344ngig)29
b(und)i(iden)n(tisc)n(h)f(v)n(erteilt)g(sind.)g(Bestimmen)h(Sie)f(die)h
(V)-7 b(erteilung)30 b(v)n(on)p 2550 1358 76 4 v 29 w
Fi(X)2625 1437 y Fg(n)2701 1425 y Fn(so)n(wie)f(den)i(Erw)n(artungsw)n
(ert)0 1524 y(und)d(die)g(V)-7 b(arianz)26 b(v)n(on)p
761 1457 V 27 w Fi(X)836 1536 y Fg(n)909 1524 y Fn(und)i
Fi(S)1131 1494 y Fh(2)1126 1545 y Fg(n)1171 1524 y Fn(.)0
1773 y Fk(Aufgab)s(e)k(2)145 b Fn(\(2)28 b(Punkte\))0
1896 y(Seien)41 b Fi(Y)278 1908 y Fh(1)315 1896 y Fi(;)14
b(Y)400 1908 y Fh(2)482 1896 y Fj(:)44 b(\012)h Ff(!)f
Fe(R)d Fn(unabh\344ngige)e(Zufallsv)-5 b(ariablen)39
b(mit)i Fi(Y)2205 1908 y Fh(1)2287 1896 y Ff(\030)j Fj(\000\()p
Fi(b;)14 b(p)2595 1908 y Fh(1)2632 1896 y Fj(\))40 b
Fn(und)h Fi(Y)2931 1908 y Fh(2)3013 1896 y Ff(\030)j
Fj(\000\()p Fi(b;)14 b(p)3321 1908 y Fh(2)3358 1896 y
Fj(\))p Fn(,)41 b(w)n(ob)r(ei)0 1996 y Fi(b;)14 b(p)115
2008 y Fh(1)152 1996 y Fi(;)g(p)231 2008 y Fh(2)291 1996
y Fi(>)22 b Fj(0)p Fn(.)27 b(Zeigen)g(Sie,)h(dass)1403
2096 y Fi(Y)1451 2108 y Fh(1)1507 2096 y Fj(+)18 b Fi(Y)1638
2108 y Fh(2)1699 2096 y Ff(\030)k Fj(\000\()p Fi(b;)14
b(p)1985 2108 y Fh(1)2041 2096 y Fj(+)k Fi(p)2166 2108
y Fh(2)2203 2096 y Fj(\))p Fn(.)0 2494 y Fk(Aufgab)s(e)32
b(3)145 b Fn(\(5)28 b(Punkte\))0 2617 y(Wir)f(b)r(etrac)n(h)n(ten)g
(eine)g(Zufallsstic)n(hprob)r(e)f Fj(\()p Fi(X)1496 2629
y Fh(1)1533 2617 y Fi(;)14 b(:)g(:)g(:)f(;)h(X)1786 2629
y Fg(n)1831 2617 y Fj(\))28 b Fn(v)n(on)e(iid)i(Stic)n(hprob)r(en)n(v)
-5 b(ariablen)25 b(mit)j Fi(X)3176 2629 y Fh(1)3236 2617
y Ff(\030)22 b Fi(N)9 b Fj(\()p Fi(\026;)14 b(\033)3568
2587 y Fh(2)3606 2617 y Fj(\))p Fn(.)0 2717 y(Zeigen)27
b(Sie,)h(dass)1489 2809 y Fj(\()p Fi(n)19 b Ff(\000)f
Fj(1\))p Fi(S)1803 2779 y Fh(2)1798 2830 y Fg(n)p 1489
2846 354 4 v 1622 2922 a Fi(\033)1672 2898 y Fh(2)1876
2865 y Ff(\030)k Fi(\037)2015 2831 y Fh(2)2015 2886 y
Fg(n)p Fd(\000)p Fh(1)2159 2865 y Fi(;)0 3038 y Fn(w)n(ob)r(ei)1326
3183 y Fi(S)1382 3149 y Fh(2)1377 3203 y Fg(n)1445 3183
y Fj(=)1618 3127 y(1)p 1542 3164 193 4 v 1542 3240 a
Fi(n)d Ff(\000)f Fj(1)1798 3079 y Fg(n)1759 3104 y Fc(X)1765
3281 y Fg(i)p Fh(=1)1879 3183 y Fj(\()p Fi(X)1980 3195
y Fg(i)2026 3183 y Ff(\000)p 2109 3116 76 4 v 18 w Fi(X)2184
3195 y Fg(n)2229 3183 y Fj(\))2261 3149 y Fh(2)2313 3183
y Fi(:)0 3421 y Fn(Hin)n(w)n(eis:)27 b(Ben)n(utzen)h(sie,)f(dass)p
1020 3354 V 27 w Fi(X)1095 3433 y Fg(n)1168 3421 y Fn(und)h
Fi(S)1390 3391 y Fh(2)1385 3441 y Fg(n)1458 3421 y Fn(unabh\344ngig)e
(sind.)0 3670 y Fk(Aufgab)s(e)32 b(4)145 b Fn(\()28 b(4)f(+)h(3)f(+)g
(4)g(Punkte\))0 3793 y(Sei)h Fi(U)191 3805 y Fg(r)250
3793 y Fj(:)23 b(\012)g Ff(!)g Fe(R)28 b Fn(eine)g Fi(\037)796
3763 y Fh(2)796 3813 y Fg(r)833 3793 y Fn(\025v)n(erteilte)e(Zufallsv)
-5 b(ariable.)60 3967 y(\(a\))42 b(Zeigen)26 b(Sie,)i(dass)f
Fj(lim)923 3979 y Fg(r)r Fd(!1)1106 3967 y Fi(P)1185
3875 y Fc(\020)1244 3933 y Fg(U)1289 3941 y Fb(r)1323
3933 y Fd(\000)p Fg(r)p 1244 3948 164 4 v 1266 3957 a
Fd(p)p 1320 3957 66 3 v 1320 4005 a Fh(2)p Fg(r)1441
3967 y Ff(\024)22 b Fi(z)1571 3875 y Fc(\021)1643 3967
y Fj(=)1731 3900 y Fc(R)1786 3921 y Fg(z)1770 3997 y
Fd(\0001)1964 3934 y Fh(1)p 1916 3948 129 4 v 1916 3957
a Fd(p)p 1971 3957 75 3 v 48 x Fh(2)p Fg(\031)2055 3967
y Fi(e)2094 3937 y Fd(\000)p Fg(y)2182 3912 y Fa(2)2213
3937 y Fg(=)p Fh(2)2285 3967 y Fi(dy)30 b Fn(f\374r)e(jedes)f
Fi(z)g Ff(2)c Fe(R)28 b Fn(gilt.)55 4141 y(\(b\))43 b(V)-7
b(erw)n(enden)27 b(Sie)g(\(a\),)h(um)g(zu)g(zeigen,)f(dass)g(f\374r)g
(jedes)h Fi(z)e Ff(2)e Fe(R)984 4371 y Fj(lim)959 4421
y Fg(r)r Fd(!1)1138 4371 y Fi(P)1217 4279 y Fc(\020)1267
4295 y(p)p 1350 4295 135 4 v 76 x Fj(2)p Fi(U)1449 4383
y Fg(r)1503 4371 y Ff(\000)1586 4302 y(p)p 1655 4302
225 4 v 69 x Fj(2)p Fi(r)d Ff(\000)d Fj(1)k Ff(\024)h
Fi(z)2033 4279 y Fc(\021)2105 4371 y Fj(=)2193 4258 y
Fc(Z)2276 4279 y Fg(z)2239 4447 y Fd(\0001)2445 4315
y Fj(1)p 2385 4352 161 4 v 2385 4369 a Ff(p)p 2454 4369
92 4 v 68 x Fj(2)p Fi(\031)2556 4371 y(e)2595 4337 y
Fd(\000)p Fg(y)2683 4312 y Fa(2)2714 4337 y Fg(=)p Fh(2)2786
4371 y Fi(dy)16 b(:)65 4657 y Fn(\(c\))42 b(F\374r)28
b Fi(r)h Fj(=)c(25)j Fn(erh\344lt)g(man)h Fi(P)12 b Fj(\()p
Fi(U)1218 4669 y Fh(25)1314 4657 y Ff(\024)25 b Fj(34)p
Fi(:)p Fj(382\))e(=)i(0)p Fi(:)p Fj(90)p Fn(.)j(V)-7
b(ergleic)n(hen)28 b(Sie)h(die)g(W)-7 b(ahrsc)n(heinlic)n(hk)n(eit)28
b Fj(0)p Fi(:)p Fj(9)g Fn(mit)208 4757 y(den)c(N\344herungsw)n(erten,)f
(die)h(sic)n(h)g(aus)g(T)-7 b(eil)25 b(\(a\))g(bzw.)f(\(b\))h(f\374r)g
Fi(P)12 b Fj(\()p Fi(U)2373 4769 y Fh(25)2466 4757 y
Ff(\024)23 b Fj(34)p Fi(:)p Fj(382\))e(=)h(0)p Fi(:)p
Fj(90)h Fn(ergeb)r(en.)h(Zeigen)208 4856 y(Sie)j(hierzu)h(zun\344c)n
(hst)f(mit)h(Hilfe)g(v)n(on)f(\(b\),)h(dass)1063 5048
y Fi(P)12 b Fj(\()p Fi(U)1217 5060 y Fg(r)1276 5048 y
Ff(\024)23 b Fi(z)t Fj(\))g Ff(\031)f Fj(\010\()1641
4975 y Ff(p)p 1711 4975 84 4 v 1711 5048 a Fj(2)p Fi(z)f
Ff(\000)1896 4978 y(p)p 1965 4978 225 4 v 70 x Fj(2)p
Fi(r)g Ff(\000)d Fj(1)o(\))167 b Fn(f\374r)83 b Fi(z)26
b(>)d Fj(0)14 b Fi(;)208 5230 y Fn(w)n(ob)r(ei)21 b Fj(\010)h
Fn(die)g(V)-7 b(erteilungsfunktion)21 b(der)h(Standardnormalv)n
(erteilung)d(ist.)j(Hin)n(w)n(eis:)f Fj(\010\(1)p Fi(:)p
Fj(3268\))g(=)i(0)p Fi(:)p Fj(9077)p Fn(,)208 5330 y
Fj(\010\(1)p Fi(:)p Fj(2924\))e(=)h(0)p Fi(:)p Fj(9019)p
Fn(.)p eop end
%%Trailer

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