Concepts of Probability Theory (eBook)

Second Revised Edition

Paul E. Pfeiffer (Autor)

eBook Download: EPUB

2013 | 2., Second Edition, Revised
416 Seiten
Dover Publications (Verlag)
9780486165660 (ISBN)

Infos

Using the Kolmogorov model, this intermediate-level text discusses random variables, probability distributions, mathematical expectation, random processes, more. For advanced undergraduates students of science, engineering, or math. Includes problems with answers and six appendixes. 1965 edition.

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This approach to the basics of probability theory employs the simple conceptual framework of the Kolmogorov model, a method that comprises both the literature of applications and the literature on pure mathematics. The author also presents a substantial introduction to the idea of a random process. Intended for college juniors and seniors majoring in science, engineering, or mathematics, the book assumes a familiarity with basic calculus.After a brief historical introduction, the text examines a mathematical model for probability, random variables and probability distributions, sums and integrals, mathematical expectation, sequence and sums of random variables, and random processes. Problems with answers conclude each chapter, and six appendixes offer supplementary material. This text provides an excellent background for further study of statistical decision theory, reliability theory, dynamic programming, statistical game theory, coding and information theory, and classical sampling statistics.

Autor

Paul E. Pfeiffer is Professor Emeritus of Computational and Applied Mathematics at Rice University. His research interests coincide with his teaching interests: electronic circuits, control systems, analog computers, switching circuits, coding theory, applied probability, and random processes.

Inhalt

PrefaceChapter 1. Introduction1-1. Basic Ideas and the Classical Definition1-2. Motivation for a More General Theory Selected ReferencesChapter 2. A Mathematical Model for Probability2-1. In Search of a Model2-2. A Model for Events and Their Occurrence2-3. A Formal Definition of Probability2-4. An Auxiliary Model-Probability as Mass2-5. Conditional Probability2-6. Independence in Probabililty Theory2-7. Some Techniques for Handling Events2-8. Further Results on Independent Events2-9. Some Comments on Strategy Problems Selected ReferencesChapter 3. Random Variables and Probability Distributions3-1. Random Variables and Events3-2. Random Variables and Mass Distributions3-3. Discrete Random Variables3-4. Probability Distribution Functions3-5. Families of Random Variables and Vector-valued Random Variables3-6. Joint Distribution Functions3-7. Independent Random Variables3-8. Functions of Random Variables3-9. Distributions for Functions of Random Variables3-10. Almost-sure Relationships Problems Selected ReferencesChapter 4. Sums and Integrals4-1. Integrals of Riemann and Lebesque4-2. Integral of a Simple Random Variable4-3. Some Basic Limit Theorems4-4. Integrable Random Variables4-5. The Lebesgue-Stieltjes Integral4-6. Transformation of Integrals Selected ReferencesChapter 5. Mathematical Expectation5-1. Definition and Fundamental Formulas5-2. Some Properties of Mathematical Expectation5-3. The Mean Value of a Random Variable5-4. Variance and Standard Deviation5-5. Random Samples and Random Variables5-6. Probability and Information5-7. Moment-generating and Characteristic Functions Problems Selected ReferencesChapter 6. Sequences and Sums of Random Variables6-1. Law of Large Numbers (Weak Form)6-2. Bounds on Sums of Independent Random Variables6-3. Types of Convergence6-4. The Strong Law of Large Numbers6-5. The Central Limit Theorem Problems Selected ReferencesChapter 7. Random Processes7-1. The General Concept of a Random Process7-2. Constant Markov Chains7-3. Increments of Processes; The Poisson Process7-4. Distribution Functions for Random Processes7-5. Processes Consisting of Step Functions7-6. Expectations; Correlation and Covariance Functions7-7. Stationary Random Processes7-8. Expectations and Time Averages; Typical Functions7-9. Gaussian Random Processes Problems Selected ReferencesAppendixes Appendix A. Some Elements of Combinatorial Analysis Appendix B. Some Topics in Set Theory Appendix C. Measurability of Functions Appendix D. Proofs of Some Theorems Appendix E. Integrals of Complex-valued Random Variables Appendix F. Summary of Properties and Key TheoremsBIBLIOGRAPHYINDEX

Produkt-Details

• Erscheint lt. Verlag: 13.5.2013
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Maße: 140 x 140 mm
• Gewicht: 454 g
• Themenwelt: Mathematik / Informatik ► Mathematik
• Schlagworte: Kolmogorov Model • Probability Theory • Random Process
• ISBN-13: 9780486165660 / 9780486165660