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, and more. Includes 150 problems, many with answers.
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, and more. Includes 150 problems, many with answers.
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 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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