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Full 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.
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
