Probability Theory (Dover Publications Inc.)

1 BASIC CONCEPTS 1. Probability and Relative Frequency 2. Rudiments of Combinatorial Analysis Problems2 COMBINATION OF EVENTS 3. Elementary Events. The Sample Space 4. The Addition Law for Probabilities Problems3 DEPENDENT EVENTS 5.

Conditional Probability 6. Statistical Independence Problems4 RANDOM VARIABLES 7. Discrete and Continuous Random Variables. Distribution Functions 8. Mathematical Expectation 9. Chebyshev's Inequality.

The Variance and Correlation Coefficient Problems5 THREE IMPORTANT PROBABILITY DISTRIBUTIONS 10. Bernoulli Trials. The Binomial and Poisson Distributions 11. The De Moivre-Laplace Theorem. The Normal Distribution Problems6 SOME LIMIT THEOREMS 12.

The Law of Large Numbers 13. Generating Functions. Weak Convergence of Probability Distributions 14. Characteristic Functions. The Central Limit Theorem Problems7 MARKOV CHAINS 15. Transition Probabilities 16.

Persistent and Transient States 17. Limiting Probabilities. Stationary Distributions Problems8 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