Probability theory. A concise course

Cover......Page 1
S Title......Page 2
Title......Page 3
Copyright......Page 4
Editor\'s Preface......Page 5
Contents......Page 6
I. Probability and Relative Frequency ......Page 9
2. Rudiments of Combinatorial Analysis ......Page 12
PROBLEMS ......Page 18
3. Elementary Events. The Sample Space ......Page 21
4. The Addition Law for Probabilities ......Page 24
PROBLEMS ......Page 30
5. Conditional Probability ......Page 33
6. Statistical Independence ......Page 38
PROBLEMS ......Page 42
7. Discrete and Continuous Random Variables Distribution Functions......Page 45
8. Mathematical Expectation ......Page 52
9. Chebyshev\'s Inequality. The Variance and  Correlation Coefficient......Page 56
PROBLEMS ......Page 58
10. Bernoulli Trials. The Binomial and Poisson Distributions ......Page 62
II. The De Moivre-Laplace Theorem. The Normal Distribution ......Page 67
PROBLEMS ......Page 73
12. The Law of Large Numbers ......Page 76
13. Generating Functions. Weak Convergence of Probability Distributions......Page 78
14. Characteristic Functions. The Central Limit Theorem ......Page 83
PROBLEMS ......Page 88
15. Transition Probabilities ......Page 91
16. Persistent and Transient States ......Page 95
17. Limiting Probabilities. Stationary Distributions ......Page 101
PROBLEMS ......Page 106
18. Definitions. The Sojourn Time ......Page 110
19. The Kolmogorov Equations ......Page 113
20. More on limiting Probabilities. Erlang\'s Formula ......Page 117
PROBLEMS ......Page 120
Appendix 1: Information Theory......Page 123
PROBLEMS ......Page 127
Appendix 2 : Game Theory......Page 129
PROBLEMS ......Page 134
Appendix 3: Branching Processes......Page 135
PROBLEMS ......Page 142
Appendix 4: Problems of Optimal Control ......Page 144
PROBLEMS ......Page 150
Bibliography......Page 151
Index......Page 153
Back Cover......Page 157