Probability Theory: A Concise Course

Overview

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.

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Probability Theory: A Concise Course

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Overview

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.

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Product Details

  • ISBN-13: 9780486635446
  • Publisher: Dover Publications
  • Publication date: 6/1/1977
  • Series: Dover Books on Mathematics Series
  • Edition description: Rev. English ed
  • Edition number: 1
  • Pages: 148
  • Sales rank: 324,284
  • Product dimensions: 5.66 (w) x 8.18 (h) x 0.33 (d)

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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