Roussas Introduction to Probability

1. Auflage 2006
ISBN: 978-0-08-050933-4
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 400 Seiten, Web PDF

Roussas's Introduction to Probability features exceptionally clear explanations of the mathematics of probability theory and explores its diverse applications through numerous interesting and motivational examples. It provides a thorough introduction to the subject for professionals and advanced students taking their first course in probability. The content is based on the introductory chapters of Roussas's book, An Intoduction to Probability and Statistical Inference, with additional chapters and revisions.
• Written by a well-respected author known for great exposition and readability
• Boasts many real world examples
• Pedagogy includes chapter summaries, tables of distributions and formulas, and answers to even-numbered exercises

George G. Roussas earned a B.S. in Mathematics with honors from the University of Athens, Greece, and a Ph.D. in Statistics from the University of California, Berkeley. As of July 2014, he is a Distinguished Professor Emeritus of Statistics at the University of California, Davis. Roussas is the author of five books, the author or co-author of five special volumes, and the author or co-author of dozens of research articles published in leading journals and special volumes. He is a Fellow of the following professional societies: The American Statistical Association (ASA), the Institute of Mathematical Statistics (IMS), The Royal Statistical Society (RSS), the American Association for the Advancement of Science (AAAS), and an Elected Member of the International Statistical Institute (ISI); also, he is a Corresponding Member of the Academy of Athens. Roussas was an associate editor of four journals since their inception, and is now a member of the Editorial Board of the journal Statistical Inference for Stochastic Processes. Throughout his career, Roussas served as Dean, Vice President for Academic Affairs, and Chancellor at two universities; also, he served as an Associate Dean at UC-Davis, helping to transform that institution's statistical unit into one of national and international renown. Roussas has been honored with a Festschrift, and he has given featured interviews for the Statistical Science and the Statistical Periscope. He has contributed an obituary to the IMS Bulletin for Professor-Academician David Blackwell of UC-Berkeley, and has been the coordinating editor of an extensive article of contributions for Professor Blackwell, which was published in the Notices of the American Mathematical Society and the Celebratio Mathematica.

Autoren/Hrsg.

Roussas, George G.

Inhaltsverzeichnis

1;Front cover;1
2;Title page;2
3;Copyright page;3
4;Table of contents;6
5;Preface;10
5.1;Overview;10
5.2;Chapter Descriptions;10
5.3;Features;12
5.4;Concluding Comments;13
6;1 Some Motivating Examples;14
7;2 Some Fundamental Concepts;19
7.1;2.1 Some Fundamental Concepts;19
7.2;2.2 Some Fundamental Results;24
7.3;2.3 Random Variables;32
7.4;2.4 Basic Concepts and Results in Counting;36
8;3 The Concept of Probability and Basic Results;44
8.1;3.1 Definition of Probability;44
8.2;3.2 Some Basic Properties and Results;49
8.3;3.3 Distribution of a Random Variable;58
9;4 Conditional Probability and Independence;69
9.1;4.1 Conditional Probability and Related Results;69
9.2;4.2 Independent Events and Related Results;82
10;5 Numerical Characteristics of a Random Variable;95
10.1;5.1 Expectation, Variance, and Moment-Generating Function of a Random Variable;95
10.2;5.2 Some Probability Inequalities;106
10.3;5.3 Median and Mode of a Random Variable;109
11;6 Some Special Distributions;116
11.1;6.1 Some Special Discrete Distributions;116
11.2;6.2 Some Special Continuous Distributions;134
12;7 Joint Probability Density Function of Two Random Variables and Related Quantities;153
12.1;7.1 Joint d.f. and Joint p.d.f. of Two Random Variables;153
12.2;7.2 Marginal and Conditional p.d.f.’s, Conditional Expectation, and Variance;165
13;8 Joint Moment-Generating Function, Covariance, and Correlation Coefficient of Two Random Variables;180
13.1;8.1 The Joint m.g.f. of Two Random Variables;180
13.2;8.2 Covariance and Correlation Coefficient of Two Random Variables;185
13.3;8.3 Proof of Theorem 1, Some Further Results;193
14;9 Some Generalizations to k Random Variables, and Three Multivariate Distributions;198
14.1;9.1 Joint Distribution of k Random Variables and Related Quantities;199
14.2;9.2 Multinomial Distribution;202
14.3;9.3 Bivariate Normal Distribution;210
14.4;9.4 Multivariate Normal Distribution;219
15;10 Independence of Random Variables and Some Applications;220
15.1;10.1 Independence of Random Variables and Criteria of Independence;220
15.2;10.2 The Reproductive Property of Certain Distributions;233
15.3;10.3 Distribution of the Sample Variance under Normality;242
16;11 Transformation of Random Variables;245
16.1;11.1 Transforming a Single Random Variable;245
16.2;11.2 Transforming Two or More Random Variables;253
16.3;11.3 Linear Transformations;268
16.4;11.4 The Probability Integral Transform;278
16.5;11.5 Order Statistics;280
17;12 Two Modes of Convergence, the Weak Law of Large Numbers, the Central Limit Theorem, and Further Results;291
17.1;12.1 Convergence in Distribution and in Probability;292
17.2;12.2 The Weak Law of Large Numbers and the Central Limit Theorem;298
17.3;12.3 Further Limit Theorems;316
18;13 An Overview of Statistical Inference;322
18.1;13.1 The Basics of Point Estimation;323
18.2;13.2 The Basics of Interval Estimation;326
18.3;13.3 The Basics of Testing Hypotheses;327
18.4;13.4 The Basics of Regression Analysis;331
18.5;13.5 The Basics of Analysis of Variance;332
18.6;13.6 The Basics of Nonparametric Inference;334
19;Appendix;337
20;Some Notations and Abbreviations;357
21;Answers to Even-Numbered Exercises;360
21.1;Chapter 2;360
21.2;Chapter 3;363
21.3;Chapter 4;367
21.4;Chapter 5;371
21.5;Chapter 6;372
21.6;Chapter 7;376
21.7;Chapter 8;378
21.8;Chapter 9;381
21.9;Chapter 10;385
21.10;Chapter 11;389
21.11;Chapter 12;391
22;INDEX;394