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Stat 5101 Lecture NotesCharles J. G
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Contents1 Random Variables and Chan
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CONTENTSv5.1.4 Variance Matrices ..
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CONTENTSviiD Relations Among Brand
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Chapter 1Random Variables andChange
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1.1. RANDOM VARIABLES 3Sometimes it
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1.1. RANDOM VARIABLES 5that is, X i
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1.2. CHANGE OF VARIABLES 7the union
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1.2. CHANGE OF VARIABLES 9Thus even
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1.2. CHANGE OF VARIABLES 11Every in
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1.2. CHANGE OF VARIABLES 13where f
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1.3. RANDOM VECTORS 151.3.1 Discret
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1.4. THE SUPPORT OF A RANDOM VARIAB
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1.5. JOINT AND MARGINAL DISTRIBUTIO
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1.5. JOINT AND MARGINAL DISTRIBUTIO
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1.6. MULTIVARIABLE CHANGE OF VARIAB
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1.6. MULTIVARIABLE CHANGE OF VARIAB
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1.6. MULTIVARIABLE CHANGE OF VARIAB
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1.6. MULTIVARIABLE CHANGE OF VARIAB
- Page 39 and 40: Chapter 2Expectation2.1 Introductio
- Page 41 and 42: 2.3. BASIC PROPERTIES 33expectation
- Page 43 and 44: 2.3. BASIC PROPERTIES 35that is, th
- Page 45 and 46: 2.4. MOMENTS 37The Multiplicativity
- Page 47 and 48: 2.4. MOMENTS 39holds for all real-v
- Page 49 and 50: 2.4. MOMENTS 41simple, it is often
- Page 51 and 52: 2.4. MOMENTS 43In contrast, for all
- Page 53 and 54: 2.4. MOMENTS 45is the sum of the ex
- Page 55 and 56: 2.4. MOMENTS 47Proof. Just take a i
- Page 57 and 58: 2.4. MOMENTS 49What happens to Coro
- Page 59 and 60: 2.4. MOMENTS 51This inequality is a
- Page 61 and 62: 2.4. MOMENTS 53(a)Why does (2.7) as
- Page 63 and 64: 2.5. PROBABILITY THEORY AS LINEAR A
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- Page 83 and 84: 2.6. PROBABILITY IS A SPECIAL CASE
- Page 85 and 86: 2.7. INDEPENDENCE 772.7 Independenc
- Page 87 and 88: 2.7. INDEPENDENCE 79Then X and Y ar
- Page 89: 2.7. INDEPENDENCE 81Show that the f
- Page 93 and 94: 3.1. PARAMETRIC FAMILIES OF DISTRIB
- Page 95 and 96: 3.2. CONDITIONAL PROBABILITY DISTRI
- Page 97 and 98: 3.3. AXIOMS FOR CONDITIONAL EXPECTA
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- Page 119 and 120: Chapter 4Parametric Families ofDist
- Page 121 and 122: 4.1. LOCATION-SCALE FAMILIES 113The
- Page 123 and 124: 4.2. THE GAMMA DISTRIBUTION 115Show
- Page 125 and 126: 4.3. THE BETA DISTRIBUTION 117cours
- Page 127 and 128: 4.4. THE POISSON PROCESS 119Hence t
- Page 129 and 130: 4.4. THE POISSON PROCESS 121Definit
- Page 131 and 132: 4.4. THE POISSON PROCESS 123measure
- Page 133 and 134: 4.4. THE POISSON PROCESS 1254-3. A
- Page 135 and 136: Chapter 5Multivariate DistributionT
- Page 137 and 138: 5.1. RANDOM VECTORS 129Again like r
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5.1. RANDOM VECTORS 1335.1.7 Linear
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5.1. RANDOM VECTORS 135Example 5.1.
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5.1. RANDOM VECTORS 137Example 5.1.
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5.1. RANDOM VECTORS 139where we hav
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5.2. THE MULTIVARIATE NORMAL DISTRI
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5.2. THE MULTIVARIATE NORMAL DISTRI
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5.2. THE MULTIVARIATE NORMAL DISTRI
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5.2. THE MULTIVARIATE NORMAL DISTRI
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5.2. THE MULTIVARIATE NORMAL DISTRI
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5.3. BERNOULLI RANDOM VECTORS 151Th
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5.3. BERNOULLI RANDOM VECTORS 153yo
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5.4. THE MULTINOMIAL DISTRIBUTION 1
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5.4. THE MULTINOMIAL DISTRIBUTION 1
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5.4. THE MULTINOMIAL DISTRIBUTION 1
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5.4. THE MULTINOMIAL DISTRIBUTION 1
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5.4. THE MULTINOMIAL DISTRIBUTION 1
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Chapter 6Convergence Concepts6.1 Un
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6.1. UNIVARIATE THEORY 167It simpli
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6.1. UNIVARIATE THEORY 169density o
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6.1. UNIVARIATE THEORY 171Rewriting
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6.1. UNIVARIATE THEORY 173Comment T
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6.1. UNIVARIATE THEORY 175Problems6
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Chapter 7Sampling Theory7.1 Empiric
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7.1. EMPIRICAL DISTRIBUTIONS 1797.1
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7.1. EMPIRICAL DISTRIBUTIONS 181Def
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7.1. EMPIRICAL DISTRIBUTIONS 183To
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7.2. SAMPLES AND POPULATIONS 185The
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7.2. SAMPLES AND POPULATIONS 187•
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7.3. SAMPLING DISTRIBUTIONS OF SAMP
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7.3. SAMPLING DISTRIBUTIONS OF SAMP
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7.3. SAMPLING DISTRIBUTIONS OF SAMP
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7.3. SAMPLING DISTRIBUTIONS OF SAMP
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7.3. SAMPLING DISTRIBUTIONS OF SAMP
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7.3. SAMPLING DISTRIBUTIONS OF SAMP
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7.3. SAMPLING DISTRIBUTIONS OF SAMP
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7.3. SAMPLING DISTRIBUTIONS OF SAMP
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7.4. SAMPLING DISTRIBUTIONS OF SAMP
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7.4. SAMPLING DISTRIBUTIONS OF SAMP
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7.4. SAMPLING DISTRIBUTIONS OF SAMP
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Appendix AGreek LettersTable A.1: T
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Appendix BSummary of Brand-NameDist
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B.1. DISCRETE DISTRIBUTIONS 215B.1.
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B.2. CONTINUOUS DISTRIBUTIONS 217Th
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B.2. CONTINUOUS DISTRIBUTIONS 219B.
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B.4. DISCRETE MULTIVARIATE DISTRIBU
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B.5. CONTINUOUS MULTIVARIATE DISTRI
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B.5. CONTINUOUS MULTIVARIATE DISTRI
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Appendix CAddition Rules forDistrib
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Appendix DRelations Among BrandName
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Appendix EEigenvalues andEigenvecto
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E.2. EIGENVALUES AND EIGENVECTORS 2
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E.2. EIGENVALUES AND EIGENVECTORS 2
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E.3. POSITIVE DEFINITE MATRICES 237
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Appendix FNormal Approximations for