Probability and information: an integrated approach
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2008
|
| Ausgabe: | second edition |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xvi, 273 Seiten Diagramme |
| ISBN: | 9780521727884 9780521899048 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Contents
Preface to the second edition page xi
Preface to the first edition xiii
1 Introduction 1
1.1 Chance and information 1
1.2 Mathematical models of chance phenomena 2
1.3 Mathematical structure and mathematical proof 5
1.4 Plan of this book 7
2 Combinatorics 10
2.1 Counting 10
2.2 Arrangements 11
2.3 Combinations 13
2.4 Multinomial coefficients 16
2.5 The gamma function 18
Exercises 19
Further reading 21
3 Sets and measures 22
3.1 The concept of a set 22
3.2 Set operations 25
3.3 Boolean algebras 29
3.4 Measures on Boolean algebras 32
Exercises 37
Further reading 40
4 Probability 41
4.1 The concept of probability 41
4.2 Probability in practice 43
vn
viii Contents
4.3 Conditional probability 48
4.4 Independence 55
4.5 The interpretation of probability 57
4.6 The historical roots of probability 62
Exercises 64
Further reading 68
5 Discrete random variables 70
5.1 The concept of a random variable 70
5.2 Properties of random variables 72
5.3 Expectation and variance 78
5.4 Covariance and correlation 83
5.5 Independent random variables 86
5.6 I.I.D. random variables 89
5.7 Binomial and Poisson random variables 91
5.8 Geometric, negative binomial and hypergeometric
random variables 95
Exercises 99
Further reading 104
6 Information and entropy 105
6.1 What is information? 105
6.2 Entropy 108
6.3 Joint and conditional entropies; mutual information 111
6.4 The maximum entropy principle 115
6.5 Entropy, physics and life 117
6.6 The uniqueness of entropy 119
Exercises 123
Further reading 125
7 Communication 127
7.1 Transmission of information 127
7.2 The channel capacity 130
7.3 Codes 132
7.4 Noiseless coding 137
7.5 Coding and transmission with noise - Shannon s
theorem 143
7.6 Brief remarks about the history of information theory 150
Exercises 151
Further reading 153
Contents ix
8 Random variables with probability density functions 155
8.1 Random variables with continuous ranges 155
8.2 Probability density functions 157
8.3 Discretisation and integration 161
8.4 Laws of large numbers 164
8.5 Normal random variables 167
8.6 The central limit theorem 172
8.7 Entropy in the continuous case 179
Exercises 182
Further reading 186
9 Random vectors 188
9.1 Cartesian products 188
9.2 Boolean algebras and measures on products 191
9.3 Distributions of random vectors 193
9.4 Marginal distributions 199
9.5 Independence revisited 201
9.6 Conditional densities and conditional entropy 204
9.7 Mutual information and channel capacity 208
Exercises 212
Further reading 216
10 Markov chains and their entropy 217
10.1 Stochastic processes 217
10.2 Markov chains 219
10.3 The Chapman-Kolmogorov equations 224
10.4 Stationary processes 227
10.5 Invariant distributions and stationary Markov chains 229
10.6 Entropy rates for Markov chains 235
Exercises 240
Further reading 243
Exploring further 245
Appendix 1 Proof by mathematical induction 247
Appendix 2 Lagrange multipliers 249
Appendix 3 Integration of exp (— ^jc2) 252
Appendix 4 Table of probabilities associated with the standard
normal distribution 254
Appendix 5 A rapid review of matrix algebra 256
Selected solutions 260
Index 268
|
| adam_txt |
Contents
Preface to the second edition page xi
Preface to the first edition xiii
1 Introduction 1
1.1 Chance and information 1
1.2 Mathematical models of chance phenomena 2
1.3 Mathematical structure and mathematical proof 5
1.4 Plan of this book 7
2 Combinatorics 10
2.1 Counting 10
2.2 Arrangements 11
2.3 Combinations 13
2.4 Multinomial coefficients 16
2.5 The gamma function 18
Exercises 19
Further reading 21
3 Sets and measures 22
3.1 The concept of a set 22
3.2 Set operations 25
3.3 Boolean algebras 29
3.4 Measures on Boolean algebras 32
Exercises 37
Further reading 40
4 Probability 41
4.1 The concept of probability 41
4.2 Probability in practice 43
vn
viii Contents
4.3 Conditional probability 48
4.4 Independence 55
4.5 The interpretation of probability 57
4.6 The historical roots of probability 62
Exercises 64
Further reading 68
5 Discrete random variables 70
5.1 The concept of a random variable 70
5.2 Properties of random variables 72
5.3 Expectation and variance 78
5.4 Covariance and correlation 83
5.5 Independent random variables 86
5.6 I.I.D. random variables 89
5.7 Binomial and Poisson random variables 91
5.8 Geometric, negative binomial and hypergeometric
random variables 95
Exercises 99
Further reading 104
6 Information and entropy 105
6.1 What is information? 105
6.2 Entropy 108
6.3 Joint and conditional entropies; mutual information 111
6.4 The maximum entropy principle 115
6.5 Entropy, physics and life 117
6.6 The uniqueness of entropy 119
Exercises 123
Further reading 125
7 Communication 127
7.1 Transmission of information 127
7.2 The channel capacity 130
7.3 Codes 132
7.4 Noiseless coding 137
7.5 Coding and transmission with noise - Shannon's
theorem 143
7.6 Brief remarks about the history of information theory 150
Exercises 151
Further reading 153
Contents ix
8 Random variables with probability density functions 155
8.1 Random variables with continuous ranges 155
8.2 Probability density functions 157
8.3 Discretisation and integration 161
8.4 Laws of large numbers 164
8.5 Normal random variables 167
8.6 The central limit theorem 172
8.7 Entropy in the continuous case 179
Exercises 182
Further reading 186
9 Random vectors 188
9.1 Cartesian products 188
9.2 Boolean algebras and measures on products 191
9.3 Distributions of random vectors 193
9.4 Marginal distributions 199
9.5 Independence revisited 201
9.6 Conditional densities and conditional entropy 204
9.7 Mutual information and channel capacity 208
Exercises 212
Further reading 216
10 Markov chains and their entropy 217
10.1 Stochastic processes 217
10.2 Markov chains 219
10.3 The Chapman-Kolmogorov equations 224
10.4 Stationary processes 227
10.5 Invariant distributions and stationary Markov chains 229
10.6 Entropy rates for Markov chains 235
Exercises 240
Further reading 243
Exploring further 245
Appendix 1 Proof by mathematical induction 247
Appendix 2 Lagrange multipliers 249
Appendix 3 Integration of exp (— ^jc2) 252
Appendix 4 Table of probabilities associated with the standard
normal distribution 254
Appendix 5 A rapid review of matrix algebra 256
Selected solutions 260
Index 268 |
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| spelling | Applebaum, David 1956- (DE-588)136277659 aut Probability and information an integrated approach David Applebaum second edition Cambridge Cambridge University Press 2008 xvi, 273 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Information, Théorie de l' ram Probabilités Probabilités ram Théorie de l'information Information theory Probabilities Informationstheorie (DE-588)4026927-9 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd rswk-swf Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 Wahrscheinlichkeitstheorie (DE-588)4079013-7 s Informationstheorie (DE-588)4026927-9 s 1\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016526193&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Applebaum, David 1956- Probability and information an integrated approach Information, Théorie de l' ram Probabilités Probabilités ram Théorie de l'information Information theory Probabilities Informationstheorie (DE-588)4026927-9 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| subject_GND | (DE-588)4026927-9 (DE-588)4064324-4 (DE-588)4079013-7 |
| title | Probability and information an integrated approach |
| title_auth | Probability and information an integrated approach |
| title_exact_search | Probability and information an integrated approach |
| title_exact_search_txtP | Probability and information an integrated approach |
| title_full | Probability and information an integrated approach David Applebaum |
| title_fullStr | Probability and information an integrated approach David Applebaum |
| title_full_unstemmed | Probability and information an integrated approach David Applebaum |
| title_short | Probability and information |
| title_sort | probability and information an integrated approach |
| title_sub | an integrated approach |
| topic | Information, Théorie de l' ram Probabilités Probabilités ram Théorie de l'information Information theory Probabilities Informationstheorie (DE-588)4026927-9 gnd Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd Wahrscheinlichkeitstheorie (DE-588)4079013-7 gnd |
| topic_facet | Information, Théorie de l' Probabilités Théorie de l'information Information theory Probabilities Informationstheorie Wahrscheinlichkeitsrechnung Wahrscheinlichkeitstheorie |
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