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26 Pages
ps5
Course: STAT 521, Fall 2008School: Washington
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Word Count: 16235
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Coursehero >> Washington >> Washington >> STAT 521Course Hero has millions of student submitted documents similar to the one
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Course Hero has millions of student submitted documents similar to the one
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%%BeginFont: CMSY8 %!PS-AdobeFont-1.1: CMSY8 1.0 %%CreationDate: 1991 Aug 15 07:22:10 % 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 (CMSY8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.035 def /isFixedPitch false def end readonly def /FontName /CMSY8 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 48 /prime put readonly def /FontBBox{-30 -955 1185 779}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 49 /infinity put dup 50 /element put dup 102 /braceleft put dup 103 /braceright put dup 106 /bar put dup 107 /bardbl put readonly def /FontBBox{-29 -960 1116 775}readonly def currentdict end currentfile eexec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cleartomark %%EndFont %%BeginFont: CMMI8 %!PS-AdobeFont-1.1: CMMI8 1.100 %%CreationDate: 1996 Jul 23 07:53:54 % 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 (CMMI8) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI8 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 61 /slash put dup 105 /i put
dup 107 /k put readonly def /FontBBox{-24 -250 1110 750}readonly def currentdict end currentfile eexec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
0000000000000000000000000000000000000000000000000000000000000000 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: CMMI12 %!PS-AdobeFont-1.1: CMMI12 1.100 %%CreationDate: 1996 Jul 27 08:57:55 % 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 (CMMI12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle -14.04 def /isFixedPitch false def end readonly def /FontName /CMMI12 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 22 /mu 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 69 /E put dup 70 /F put dup 73 /I put dup 78 /N put dup 89 /Y put dup 90 /Z put dup 100 /d put dup 107 /k put dup 111 /o put dup 117 /u put dup 118 /v put
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0000000000000000000000000000000000000000000000000000000000000000 %%EndFont cleartomark %%BeginFont: CMR12 %!PS-AdobeFont-1.1: CMR12 1.0 %%CreationDate: 1991 Aug 20 16:38:05 % 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 (CMR12) readonly def /FamilyName (Computer Modern) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CMR12 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 3 /Lambda put dup 6 /Sigma put dup 12 /fi put dup 40 /parenleft put dup 41 /parenright put dup 43 /plus put dup 44 /comma put dup 45 /hyphen put dup 46 /period put dup 47 /slash 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 59 /semicolon put dup 61 /equal put dup 63 /question put dup 67 /C put dup 68 /D put dup 69 /E put dup 70 /F put dup 72 /H put dup 73 /I put dup 76 /L put dup 77 /M put dup 80 /P put dup 83 /S put dup 84 /T put
dup 87 /W put dup 91 /bracketleft put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 102 /f put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 113 /q put dup 114 /r put dup 115 /s put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 121 /y put readonly def /FontBBox{-34 -251 988 750}readonly def currentdict end currentfile eexec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Washington - STAT - 521
Statistics 522, Problem Set 5 corrected version Wellner; 2/13/2008, 2/16/2008 Reading: Wellner Shorack, PfS Due: Reminder:Chapter 11, Sections 3 - 5, pages 19 - 33. Section 11.7, pages 312 - 318. Wednesday, February 20, 2008. Midterm exam, February
Washington - STAT - 521
%!PS-Adobe-2.0 %Creator: dvips(k) 5.96 Copyright 2005 Radical Eye Software %Title: ps6.dvi %CreationDate: Fri Feb 22 10:10:58 2008 %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: CMBX12 CMR12 CMSY10 CMMI12 CMMI8 CMR8 CMMI6 CMEX
Washington - STAT - 521
Statistics 522, Problem Set 7 Wellner; 2/27/2008Reading: Shorack, PfS Shorack, PfS Due:Sections 12.1-12.3, pages 319 - 329. Sections 13.1 - 13.7, pages 367-390. Wednesday, March 5, 2008.1. Graph the rst few gnj s and hnj s introduced in the han
Washington - STAT - 521
%!PS-Adobe-2.0 %Creator: dvips(k) 5.96 Copyright 2005 Radical Eye Software %Title: ps8.dvi %CreationDate: Tue Mar 4 12:11:27 2008 %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: CMBX12 CMR12 CMMI12 CMSY10 CMSY8 CMR8 CMMI8 CMEX1
Washington - STAT - 521
Statistics 522, Problem Set 8 Wellner; 3/5/2008 Reading: Shorack, PfS Shorack, PfS Due: Reminder:Sections 12.1-12.3, pages 319 - 329. Sections 13.1 - 13.7, pages 367-390. Wednesday, March 12, 2008. Final exam, Wednesday, March 19.1. PfS, Exercise
Washington - STAT - 521
%!PS-Adobe-2.0 %Creator: dvips(k) 5.96 Copyright 2005 Radical Eye Software %Title: sol.ps1.dvi %CreationDate: Wed Jan 23 16:28:18 2008 %Pages: 7 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: CMBX12 CMR12 CMMI12 CMSY10 CMR8 CMSY8 CMR6 C
Washington - STAT - 521
Statistics 522, Problem Set 1 Solutions Wellner; 1/23/20081. PfS, exercise 3.2.3, page 42: Consider a measure space (, A, ). Let 0 |A0 for a sub eld A0 of A. Starting with indicator functions, show that Xd = Xd0 for any A0 measurable function X. S
Washington - STAT - 521
Statistics 522, Problem Set 2 Solutions Wellner; 1/31/20081. (Symmetry and conditional expectation). Let X1 , X2 , . . . be i.i.d. random variables with the same distribution as X where E|X| < . Let Sn X1 + + Xn , and dene Show that E(X1 |Gn )
Washington - STAT - 521
%!PS-Adobe-2.0 %Creator: dvips(k) 5.96 Copyright 2005 Radical Eye Software %Title: sol.ps3.dvi %CreationDate: Sat Feb 9 09:41:09 2008 %Pages: 9 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %DocumentFonts: CMBX12 CMR12 CMMI12 CMEX10 CMSY10 MSBM10 CMMI
Washington - STAT - 521
Statistics 522, Problem Set 3 Solutions Wellner; 2/7/20081. Exercise 11.6.1, page 34, Wellner, Chapter 11 notes. Prove the equivalence of (i) and (ii) in Proposition 11.2.2. Solution: Suppose that (ii) holds. Let x < 0, 1, 1 x, 0 x 1, h(x) =
Washington - STAT - 521
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Washington - STAT - 521
Statistics 522, Problem Set 4 Solutions Wellner; 2/16/20081. Suppose that Y1 , . . . , Yn be independent Bernoulli (1/2) random variables so that Xj = 2Yj 1 are independent Rademacher random variables. with EXj = 0 and V ar(Xj ) = 1. Let Sn = X1 +
Washington - STAT - 521
Statistics 522, Problem Set 5 Solutions Wellner; 2/21/20081. Exercise 11.8.7, page 55, Wellner, Chapter 11 notes. (new numbering; exercise 11.6.7, page 33, old numbering). Suppose that X and Y are independent random vectors, and that W is another r
Washington - STAT - 521
Statistics 522, Midterm Exam Wellner; 2/20/20081. (24 points). Define three of the following four terms: (a) The conditional expectation of a random variable X given a (sub-) sigma-field D. (b) Convergence in distribution of a sequence of measures
Washington - STAT - 521
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Washington - STAT - 521
Statistics 522, Midterm Exam Solutions Wellner; 2/20/20081. (24 points). Dene three of the following four terms: (a) The conditional expectation of a random variable X given a (sub-) sigma-eld D. (b) Convergence in distribution of a sequence of mea
Washington - STAT - 521
Statistics 522, Final Exam Wellner; 3/19/20081. (24 points). Dene three of the following six terms: (a) An asymptotically tight sequence {Xn } in a metric space (M, d). (b) Weak convergence of probability measures {Pn } to a probability measure P o
Washington - STAT - 521
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Washington - STAT - 521
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Washington - STAT - 521
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Washington - STAT - 521
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Washington - STAT - 521
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Washington - STAT - 521
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Washington - STAT - 521
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Washington - STAT - 521
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Washington - STAT - 521
Statistics 521, Problem Set 1 Wellner; 9/26/07Reading: Due:Shorack, PfS, Chapter 1, pages 1 - 17; Wednesday, October 3, 2007.1. (a) Suppose that {An } is an increasing sequence of algebras, i.e. An An+1 for all n 1. Show that An is an algebr
Washington - STAT - 521
Statistics 522, Problem Set 2 Wellner; 1/23/2008Reading: Shorack, PfS, Shorack, PfS, Due:Chapter 11, Sections 7-8, pages 312 - 318; Chapter 13, Sections 1-7, pages 367 - 390. Wednesday, January 30, 2008.1. (Symmetry and conditional expectation)
Washington - STAT - 521
Statistics 521, Problem Set 3 Wellner; 10/12/07Reading: Shorack, PfS, Chapter 2, section 2.5, pages 35-36; Shorack, PfS, Chapter 3, sections 3.1-3.5, pages 37 - 51. Due: Wednesday, October 17, 2007. 1. PfS, Exercise 2.2.1, page 28. 2. PfS, Exercise
Washington - STAT - 521
Statistics 521, Problem Set 4 Wellner; 10/17/2007Reading: Shorack, PfS, Chapter 3, sections 3.4 - 3.5, pages 46 - 63. Reminder: Make-up lectures on Wednesday 10/17 and Wednesday 10/27, 12:30 - 1:20 in Loew 222. Due: Wednesday, October 24, 2007. 1.
Washington - STAT - 521
Statistics 521, Problem Set 5 Wellner; 10/24/2007Reading: Shorack, PfS, Chapter 4, sections 4.1 - 4.4, pages 67 - 85. Due: Wednesday, October 31, 2007. 1. PfS, Exercise 3.4.2, page 48: Show that = 1 if and only if X - X = a(Y -Y ) for some a > 0;
Washington - STAT - 521
Statistics 521, Problem Set 6 Wellner; 10/31/2007Reminder: Midterm exam on Friday, November 9. Reading: Shorack, PfS, Chapter 4, sections 4.1 - 4.4, pages 67 - 85; Chapter 5, sections 5.1 - 5.3, pages 87 - 97. Due: Wednesday, November 7, 2007. 1. P
Washington - STAT - 521
Statistics 521, Problem Set 7 Wellner; 11/07/2007Reading: Shorack, PfS, Chapter 5, pages 87 - 102; Chapter 7, pages 121 - 132. Reminder: Midterm Exam, Friday, November 9. Due: Wednesday, November 14, 2007. 1. Let be a sigma-nite measure and let b
Washington - STAT - 521
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Washington - STAT - 521
Statistics 521, Problem Set 8 Wellner; 11/14/2007Reading: Shorack, PfS, Chapter 7, pages 121 - 136; Chapter 8, pages 165 - 171. Due: Wednesday, November 21, 2007. 1. PfS Exercise 7.4.3, page 131. Prove just the parts of these formulas involving F
Washington - STAT - 521
Statistics 521, Problem Set 9 Wellner; 11/21/2007Reading: Shorack, PfS, Chapter 8, pages 165 - 171; Shorack, PfS, Chapter 10, pages 219 - 258. Due: Wednesday, November 28, 2007 1. PfS, Exercise 5.3.1, page 94. Prove that: (a) A function X = (X1 ,
Washington - STAT - 521
Statistics 521, Problem Set 10 Wellner; 11/28/2007Reading: Shorack, PfS, Chapter 10, pages 219 - 258. Reminder: Final exam, 2:30 - 4:20, Wednesday, December 12. Due: Wednesday, December 5, 2007. 1. Let K 3 be a prime and let X and Y be independent
Washington - STAT - 521
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Washington - STAT - 521
Statistics 521, Problem Set 3 Solutions Wellner; 10/18/20071. Exercise 2.2.1, page 28. Suppose that (, A) = (R2 , B2 ) where B2 denotes the -field generated by all open subsets of the plane. Recall that this -field contains all sets of the form B
Washington - STAT - 521
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Washington - STAT - 521
Statistics 521, Problem Set 4 Solutions Wellner; 10/25/071. PfS, Exercise 2.3.3, page 32: show that Xn X if and only if Xn Xm 0. Solution: First suppose that Xn X. Then for every > 0 we have ([|Xm Xn | > ]) ([|Xm X| > /2]) + ([|Xn X| > /2])
Washington - STAT - 521
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Washington - STAT - 521
Statistics 521, Problem Set 5 Solutions Wellner; 10/31/20071. PfS, Exercise 3.4.2, page 48: Show that = 1 if and only if X X = a(Y Y ) for some a > 0; and = 1 if an only if X X = a(Y Y ) for some a < 0. Thus measure linear dependence, not depen
Washington - STAT - 521
Statistics 521, Problem Set 6 Solutions Wellner; 11/07/20071. PfS, Exercise 3.5.6, page 54, modied as follows: Suppose that f0 , f1 , . . . are 0, dened on a sigma-nite measure space (, A, ). (a) Suppose that fn d = 1 for n = 0, 1, . . ., and fn
Washington - STAT - 521
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Washington - STAT - 521
Statistics 521, Problem Set 7, Solutions Wellner; 11/23/981. Let be a sigma-nite measure and let be a nite measure on (, A). Set = ; i.e. dene : A (, ] by (A) = (A) (A). (a) Show that is a signed measure. (b) Show that (A) =A(f g)d( +
Washington - STAT - 521
Statistics 521, Problem Set 8 Solutions Wellner; 11/21/20071. PfS Exercise 7.4.3, page 131. Prove just the parts of these formulas involving F , not the parts involving F 1 . Solution: (11): Since X 0 we may write X =X X 0dt to obtainE(X) =
Washington - STAT - 521
Statistics 521, Problem Set 9 Solutions Wellner; 11/28/20071. PfS, Exercise 5.3.1, page 94. Prove that: (a) A function X = (X1 , X2 , . . .) : R is B Ameasurable if and only if each Xn is B Ameasurable. (b) If X = (X1 , X2 , . . .) is B A meas
Washington - STAT - 521
Statistics 521, Problem Set 10, Solutions Wellner; 12/6/20071. Let K 3 be a prime and let X and Y be independent random variables that are uniformly distributed on {0, 1, . . . , K 1}. For 0 n < K let Zn = (X + nY )mod(K). Show that Z0 , . . . ,
Washington - STAT - 521
Statistics 521, Midterm Exam Wellner; 11/9/20071. (24 (a) (b) (c) (d) (e)points). Dene three of the following ve terms: Convergence in probability of a sequence of random variables {Xn }. Convergence in distribution of a sequence of random variab
Washington - STAT - 521
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Washington - STAT - 521
Statistics 521, Midterm Exam Solutions Wellner; 11/9/20071. (24 (a) (b) (c) (d) (e)points). Dene three of the following ve terms: Convergence in probability of a sequence of random variables {Xn }. Convergence in distribution of a sequence of ran
Washington - STAT - 521
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Washington - STAT - 582
Statistics 582, Problem Set 2 Wellner; 1/14/2009 Reading: Lehmann and Casella, TPE, Chapter 6, section 6.4, especially pages 455 - 461 and 504-508. Chapter 4, sections 5 - 6. Due: Wednesday, January 21, 2009. 1. Human beings can be classied into one
Washington - STAT - 582
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Washington - STAT - 582
Statistics 582, Problem Set 4 Wellner; 1/28/2009Reading: Chapter 5, sections 1-6. Due: Wednesday, February 4, 2009. Reminder: Make up lectures, 11:30 - 12:20, Friday, 30 January and Monday, 2 February (in Thomson 125). 1. Let = {0, 1} = A where 0
Washington - STAT - 582
Statistics 582, Problem Set 5 Wellner; 2/4/2009Reading: Chapter 5, sections 6-8 Due: Wednesday, February 11, 2009. Reminder: Midterm Exam: Friday, February 13. 1. Let X = {0, 1}, A = = {1, 2}, and assume that the losses are given by L(1, 1) = L(2,
Washington - STAT - 582
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Washington - STAT - 582
Statistics 582, Problem Set 6 Wellner; 2/11/2009Due: Wednesday, February 18, 2009. Reminder: midterm exam, Friday February 13. Reading: Chapter 5, section 8; start reading Chapter 6 1. Consider Example 5.5.4 on pages 16 and 17 of the Chapter 5 note
Washington - STAT - 582
Statistics 582, Problem Set 7 Wellner; 2/18/2009Reading: Chapter 6, sections 6.1-6.3; Due: Wednesday, February 25, 2009. 1. Continuation of problem 3, problem set 4: Suppose that X1 , . . . , Xn are i.i.d. Exponential() (so the Xs have distribution
Washington - STAT - 582
Statistics 582, Problem Set 9 Wellner; 3/4/2009Reading: Chapter 6, sections 6.1 and 6.2 (through page 19); section 6.5 (pages 42-46). Due: Wednesday, March 11, 2009. 1. Let X and Y be independent random variables with geometric distributionsx y pX
Washington - STAT - 582
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