|  | Olofsson, Peter / Andersson, Mikael
Probability, Statistics, and Stochastic Processes
 2. Auflage Juni 2012
109,- Euro
2012. 576 Seiten, Hardcover
ISBN 978-0-470-88974-9 - John Wiley & Sons
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| Kurzbeschreibung
This book provides a unique and balanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fields that serves as a stepping stone to more advanced investigations into each area. The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and renewal theory. Many new introductory problems and exercises have also been added.
Aus dem Inhalt
Preface xi
Preface to the First Edition xiii
1 Basic Probability Theory 1
1.1 Introduction 1
1.2 Sample Spaces and Events 3
1.3 The Axioms of Probability 7
1.4 Finite Sample Spaces and Combinatorics 15
1.4.1 Combinatorics 17
1.5 Conditional Probability and Independence 27
1.6 The Law of Total Probability and Bayes' Formula 41
Problems 63
2 Random Variables 76
2.1 Introduction 76
2.2 Discrete Random Variables 77
2.3 Continuous Random Variables 82
2.4 Expected Value and Variance 95
2.5 Special Discrete Distributions 111
2.6 The Exponential Distribution 123
2.7 The Normal Distribution 127
2.8 Other Distributions 131
2.9 Location Parameters 137
2.10 The Failure Rate Function 139
Problems 144
3 Joint Distributions 156
3.1 Introduction 156
3.2 The Joint Distribution Function 156
3.3 Discrete Random Vectors 158
3.4 Jointly Continuous Random Vectors 160
3.5 Conditional Distributions and Independence 164
3.5.1 Independent Random Variables 168
3.6 Functions of Random Vectors 172
3.7 Conditional Expectation 185
3.8 Covariance and Correlation 196
3.9 The Bivariate Normal Distribution 209
3.10 Multidimensional Random Vectors 216
3.11 Generating Functions 231
3.12 The Poisson Process 240
Problems 247
4 Limit Theorems 263
4.1 Introduction 263
4.2 The Law of Large Numbers 264
4.3 The Central Limit Theorem 268
4.4 Convergence in Distribution 275
Problems 278
5 Simulation 281
5.1 Introduction 281
5.2 Random Number Generation 282
5.3 Simulation of Discrete Distributions 283
5.4 Simulation of Continuous Distributions 285
5.5 Miscellaneous 290
Problems 292
6 Statistical Inference 294
6.1 Introduction 294
6.2 Point Estimators 294
6.3 Confidence Intervals 304
6.4 Estimation Methods 312
6.5 Hypothesis Testing 327
6.6 Further Topics in Hypothesis Testing 334
6.7 Goodness of Fit 339
6.8 Bayesian Statistics 351
6.9 Nonparametric Methods 363
Problems 378
7 Linear Models 391
7.1 Introduction 391
7.2 Sampling Distributions 392
7.3 Single Sample Inference 395
7.4 Comparing Two Samples 402
7.5 Analysis of Variance 409
7.6 Linear Regression 415
7.7 The General Linear Model 431
Problems 436
8 Stochastic Processes 444
8.1 Introduction 444
8.2 Discrete -Time Markov Chains 445
8.3 Random Walks and Branching Processes 464
8.4 Continuous -Time Markov Chains 475
8.5 Martingales 494
8.6 Renewal Processes 502
8.7 Brownian Motion 509
Problems 517
Appendix A Tables 527
Appendix B Answers to Selected Problems 535
Further Reading 551
Index 553
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