Probability Theory

Probability Theory : A Concise Course

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Description

This book, a concise introduction to modern probability theory and certain of its ramifications, deals with a subject indispensable to natural scientists and mathematicians alike. Here the reader, with some knowledge of mathematics, will find an excellent treatment of the elements of probability together with numerous applications. Professor Y.A. Rozanov, an internatiionally known mathematician whose work in probability theory and stochastic processes has received wide aclaim, combines succinctness of style with a judicious selection of topics. His book is highly readable, fast-moving and self-contained.
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Product details

  • Paperback | 148 pages
  • 143 x 208 x 8mm | 174g
  • New York, United States
  • English
  • New edition
  • New edition
  • Illustrations, unspecified
  • 0486635449
  • 9780486635446
  • 27,187

Table of contents

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
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46 ratings
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3 22% (10)
2 4% (2)
1 2% (1)
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