Probability Theory
A Concise Course
Published on 28. March 2003
Book
Paperback/Softback
160 pages
978-0-486-63544-6 (ISBN)
Description
This clear exposition begins with basic concepts and moves on to combination of events, dependent events and random variables, Bernoulli trials and the De Moivre-Laplace theorem, a detailed treatment of Markov chains, continuous Markov processes, and more. Includes 150 problems, many with answers. Indispensable to mathematicians and natural scientists alike.
More details
Edition
Revised edition
Language
English
Place of publication
United States
Target group
College/higher education
Professional and scholarly
Product notice
Paperback (trade)
Unsewn / adhesive bound
Dimensions
Height: 208 mm
Width: 144 mm
Thickness: 8 mm
Weight
172 gr
ISBN-13
978-0-486-63544-6 (9780486635446)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Content
1 BASIC CONCEPTS
1. Probability and Relative Frequency
2. Rudiments of Combinatorial Analysis
Problems
2 COMBINATION OF EVENTS
3. Elementary Events. The Sample Space
4. The Addition Law for Probabilities
Problems
3 DEPENDENT EVENTS
5. Conditional Probability
6. Statistical Independence
Problems
4 RANDOM VARIABLES
7. Discrete and Continuous Random Variables. Distribution Functions
8. Mathematical Expectation
9. Chebyshev's Inequality. The Variance and Correlation
Coefficient
Problems
5 THREE IMPORTANT PROBABILITY DISTRIBUTIONS
10. Bernoulli Trials. The Binomial and Poisson Distributions
11. The De Moivre-Laplace Theorem. The Normal Distribution
Problems
6 SOME LIMIT THEOREMS
12. The Law of Large Numbers
13. Generating Functions. Weak Convergence of Probability Distributions
14. Characteristic Functions. The Central Limit Theorem
Problems
7 MARKOV CHAINS
15. Transition Probabilities
16. Persistent and Transient States
17. Limiting Probabilities. Stationary Distributions
Problems
8 CONTINUOUS MARKOV PROCESSES
18. Definitions. The Sojourn Time
19. The Kolmogorov Equations
20. More on Limiting Probabilities. Erlang's Formula
Problems
APPENDIX 1 INFORMATION THEORY
APPENDIX 2 GAME THEORY
APPENDIX 3 BRANCHING PROCESSES
APPENDIX 4 PROBLEMS OF OPTIMAL CONTROL
BIBLIOGRAPHY
INDEX
1. Probability and Relative Frequency
2. Rudiments of Combinatorial Analysis
Problems
2 COMBINATION OF EVENTS
3. Elementary Events. The Sample Space
4. The Addition Law for Probabilities
Problems
3 DEPENDENT EVENTS
5. Conditional Probability
6. Statistical Independence
Problems
4 RANDOM VARIABLES
7. Discrete and Continuous Random Variables. Distribution Functions
8. Mathematical Expectation
9. Chebyshev's Inequality. The Variance and Correlation
Coefficient
Problems
5 THREE IMPORTANT PROBABILITY DISTRIBUTIONS
10. Bernoulli Trials. The Binomial and Poisson Distributions
11. The De Moivre-Laplace Theorem. The Normal Distribution
Problems
6 SOME LIMIT THEOREMS
12. The Law of Large Numbers
13. Generating Functions. Weak Convergence of Probability Distributions
14. Characteristic Functions. The Central Limit Theorem
Problems
7 MARKOV CHAINS
15. Transition Probabilities
16. Persistent and Transient States
17. Limiting Probabilities. Stationary Distributions
Problems
8 CONTINUOUS MARKOV PROCESSES
18. Definitions. The Sojourn Time
19. The Kolmogorov Equations
20. More on Limiting Probabilities. Erlang's Formula
Problems
APPENDIX 1 INFORMATION THEORY
APPENDIX 2 GAME THEORY
APPENDIX 3 BRANCHING PROCESSES
APPENDIX 4 PROBLEMS OF OPTIMAL CONTROL
BIBLIOGRAPHY
INDEX