Elementary probability:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge
Cambridge Univ. Press
2003
|
| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Table of contents Publisher description Inhaltsverzeichnis |
| Physical Description: | XII, 524 S. graph. Darst. |
| ISBN: | 0521534283 0521833442 |
Staff View
MARC
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| 100 | 1 | |a Stirzaker, David |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Elementary probability |c David Stirzaker |
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Record in the Search Index
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| adam_text | Contents
Preface to the Second Edition page xi
0 Introduction 1
0.1 Chance 1
0.2 Models 3
0.3 Symmetry 5
0.4 The Long Run 7
0.5 Pay Offs 8
0.6 Introspection 9
0.7 FAQs 10
0.8 History 14
Appendix: Review of Elementary Mathematical Prerequisites 15
1 Probability 24
1.1 Notation and Experiments 24
1.2 Events 26
1.3 The Addition Rules for Probability 32
1.4 Properties of Probability 34
1.5 Sequences of Events 36
1.6 Remarks 37
1.7 Review and Checklist for Chapter 1 38
Worked examples and exercises 40
1.8 Example: Dice 40
1.9 Example: Urn 41
1.10 Example: Cups and Saucers 42
1.11 Example: Sixes 43
1.12 Example: Family Planning 44
1.13 Example: Craps 45
1.14 Example: Murphy s Law 46
Problems 47
2 Conditional Probability and Independence 51
2.1 Conditional Probability 51
2.2 Independence 57
2.3 Recurrence and Difference Equations 60
2.4 Remarks 62
v
vi Contents
2.5 Review and Checklist for Chapter 2 64
Worked examples and exercises 65
2.6 Example: Sudden Death 65
2.7 Example: Polya s Urn 66
2.8 Example: Complacency 67
2.9 Example: Dogfight 68
2.10 Example: Smears 69
2.11 Example: Gambler s Ruin 70
2.12 Example: Accidents and Insurance 72
2.13 Example: Protocols 73
2.14 Example: Eddington s Controversy 75
Problems 76
3 Counting 83
3.1 First Principles 83
3.2 Permutations: Ordered Selection 84
3.3 Combinations: Unordered Selection 86
3.4 Inclusion—Exclusion 87
3.5 Recurrence Relations 88
3.6 Generating Functions 90
3.7 Techniques 93
3.8 Review and Checklist for Chapter 3 95
Worked examples and exercises 97
3.9 Example: Railway Trains 97
3.10 Example: Genoese Lottery 98
3.11 Example: Ringing Birds 99
3.12 Example: Lottery 101
3.13 Example: The Manages Problem 101
3.14 Example: Identity 102
3.15 Example: Runs 103
3.16 Example: Fish 105
3.17 Example: Colouring 106
3.18 Example: Matching (Rencontres) 107
Problems 108
4 Random Variables: Distribution and Expectation 114
4.1 Random Variables 114
4.2 Distributions 115
4.3 Expectation 120
4.4 Conditional Distributions 127
4.5 Sequences of Distributions 130
4.6 Inequalities 131
4.7 Review and Checklist for Chapter 4 134
Worked examples and exercises 137
4.8 Example: Royal Oak Lottery 137
4.9 Example: Misprints 138
4.10 Example: Dog Bites: Poisson Distribution 139
Contents vii
4.11 Example: Guesswork 141
4.12 Example: Gamblers Ruined Again 142
4.13 Example: Postmen 143
4.14 Example: Acme Gadgets 144
4.15 Example: Roulette and the Martingale 145
4.16 Example: Searching 146
4.17 Example: Duelling 147
4.18 Binomial Distribution: The Long Run 149
4.19 Example: Uncertainty and Entropy 150
Problems 151
5 Random Vectors: Independence and Dependence 158
5.1 Joint Distributions 158
5.2 Independence 162
5.3 Expectation 165
5.4 Sums and Products of Random Variables: Inequalities 172
5.5 Dependence: Conditional Expectation 177
5.6 Simple Random Walk 183
5.7 Martingales 190
5.8 The Law of Averages 196
5.9 Convergence 199
5.10 Review and Checklist for Chapter 5 203
Worked examples and exercises 206
5.11 Example: Golf 206
5.12 Example: Joint Lives 208
5.13 Example: Tournament 209
5.14 Example: Congregations 210
5.15 Example: Propagation 211
5.16 Example: Information and Entropy 212
5.17 Example: Cooperation 214
5.18 Example: Strange But True 215
5.19 Example: Capture Recapture 216
5.20 Example: Visits of a Random Walk 218
5.21 Example: Ordering 219
5.22 Example: More Martingales 220
5.23 Example: Simple Random Walk Martingales 221
5.24 Example: You Can t Beat the Odds 222
5.25 Example: Matching Martingales 223
5.26 Example: Three Handed Gambler s Ruin 224
Problems 226
6 Generating Functions and Their Applications 232
6.1 Introduction 232
6.2 Moments and the Probability Generating Function 236
6.3 Sums of Independent Random Variables 239
6.4 Moment Generating Functions 245
6.5 Joint Generating Functions 247
viii Contents
6.6 Sequences 251
6.7 Regeneration 254
6.8 Random Walks 259
6.9 Review and Checklist for Chapter 6 263
Appendix: Calculus 265
Worked examples and exercises 268
6.10 Example: Gambler s Ruin and First Passages 268
6.11 Example: Fair Pairs of Dice 269
6.12 Example: Branching Process 271
6.13 Example: Geometric Branching 272
6.14 Example: Waring s Theorem: Occupancy Problems 274
6.15 Example: Bernoulli Patterns and Runs 275
6.16 Example: Waiting for Unusual Light Bulbs 277
6.17 Example: Martingales for Branching 278
6.18 Example: Wald s Identity 279
6.19 Example: Total Population in Branching 280
Problems 281
7 Continuous Random Variables 287
7.1 Density and Distribution 287
7.2 Functions of Random Variables 297
7.3 Simulation of Random Variables 301
7.4 Expectation 302
7.5 Moment Generating Functions 306
7.6 Conditional Distributions 310
7.7 Ageing and Survival 312
7.8 Stochastic Ordering 314
7.9 Random Points 315
7.10 Review and Checklist for Chapter 7 318
Worked examples and exercises 321
7.11 Example: Using a Uniform Random Variable 321
7.12 Example: Normal Distribution 323
7.13 Example: Bertrand s Paradox 324
7.14 Example: Stock Control 326
7.15 Example: Obtaining Your Visa 327
7.16 Example: Pirates 329
7.17 Example: Failure Rates 330
7.18 Example: Triangles 330
7.19 Example: Stirling s Formula 332
Problems 334
8 Jointly Continuous Random Variables 337
8.1 Joint Density and Distribution 337
8.2 Change of Variables 342
8.3 Independence 344
8.4 Sums, Products, and Quotients 348
8.5 Expectation 351
8.6 Conditional Density and Expectation 355
Contents ix
8.7 Transformations: Order Statistics 361
8.8 The Poisson Process: Martingales 364
8.9 Two Limit Theorems 368
8.10 Review and Checklist for Chapter 8 371
Worked examples and exercises 375
8.11 Example: Bivariate Normal Density 375
8.12 Example: Partitions 376
8.13 Example: Buffon s Needle 377
8.14 Example: Targets 379
8.15 Example: Gamma Densities 380
8.16 Example: Simulation The Rejection Method 381
8.17 Example: The Inspection Paradox 382
8.18 Example: von Neumann s Exponential Variable 383
8.19 Example: Maximum from Minima 385
8.20 Example: Binormal and Trinomial 387
8.21 Example: Central Limit Theorem 388
8.22 Example: Poisson Martingales 389
8.23 Example: Uniform on the Unit Cube 390
8.24 Example: Characteristic Functions 390
Problems 391
9 Markov Chains 396
9.1 The Markov Property 396
9.2 Transition Probabilities 400
9.3 First Passage Times 406
9.4 Stationary Distributions 412
9.5 The Long Run 418
9.6 Markov Chains with Continuous Parameter 425
9.7 Forward Equations: Poisson and Birth Processes 428
9.8 Forward Equations: Equilibrium 431
9.9 The Wiener Process and Diffusions 436
9.10 Review and Checklist for Chapter 9 449
Worked examples and exercises 451
9.11 Example: Crossing a Cube 451
9.12 Example: Reversible Chains 453
9.13 Example: Diffusion Models 454
9.14 Example: The Renewal Chains 456
9.15 Example: Persistence 457
9.16 Example: First Passages and Bernoulli Patterns 459
9.17 Example: Poisson Processes 461
9.18 Example: Decay 462
9.19 Example: Disasters 463
9.20 Example: The General Birth Process 465
9.21 Example: The Birth Death Process 466
9.22 Example: Wiener Process with Drift 468
9.23 Example: Markov Chain Martingales 469
9.24 Example: Wiener Process Exiting a Strip 470
x Contents
9.25 Example: Arcsine Law for Zeros 471
9.26 Example: Option Pricing: Black Scholes Formula 472
Problems 473
Appendix: Solutions and Hints for Selected Exercises and Problems 478
Further Reading 514
Index of Notation 515
Index 517
|
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| spelling | Stirzaker, David Verfasser aut Elementary probability David Stirzaker 2. ed. Cambridge Cambridge Univ. Press 2003 XII, 524 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Probabilidade (textos elementares) larpcal Probabilités Waarschijnlijkheidstheorie gtt Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd rswk-swf (DE-588)4123623-3 Lehrbuch gnd-content Wahrscheinlichkeitsrechnung (DE-588)4064324-4 s DE-604 http://www.loc.gov/catdir/toc/cam031/2002042904.html Table of contents http://www.loc.gov/catdir/description/cam031/2002042904.html Publisher description HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010110058&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Stirzaker, David Elementary probability Probabilidade (textos elementares) larpcal Probabilités Waarschijnlijkheidstheorie gtt Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| subject_GND | (DE-588)4064324-4 (DE-588)4123623-3 |
| title | Elementary probability |
| title_auth | Elementary probability |
| title_exact_search | Elementary probability |
| title_full | Elementary probability David Stirzaker |
| title_fullStr | Elementary probability David Stirzaker |
| title_full_unstemmed | Elementary probability David Stirzaker |
| title_short | Elementary probability |
| title_sort | elementary probability |
| topic | Probabilidade (textos elementares) larpcal Probabilités Waarschijnlijkheidstheorie gtt Probabilities Wahrscheinlichkeitsrechnung (DE-588)4064324-4 gnd |
| topic_facet | Probabilidade (textos elementares) Probabilités Waarschijnlijkheidstheorie Probabilities Wahrscheinlichkeitsrechnung Lehrbuch |
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