内容

目次

1. Elementary Probabilities.- 1. Combinatorics.- 2. Events and Relations among Them.- 3. Classical Definition of Probability.- 4. Conditional Probability. Independence of Events.- 5. Probability of a Sum of Events. Formula for Total Probability. Bayes’ Formula.- 6. Urn Models. Polya Urn Model.- 7. Geometric Probabilty.- 8. Bernoulli Trials. Binomoal and Multinomial Distributions.- 9. Discrete Random Variables and Their Characteristics.- 10. Normal and Poisson Approximations for the Binomial Distribution.- 2. Probability Spaces and Random Variables.- 11. General Definition of Probability and ?-Algebra of Events.- 12. Random Variables and Integration.- 13. Conditional Probability, Independence and Martingales.- 14. Product of Measurable Spaces and Probabilities on Them.- 3. Characteristics of Random Variables.- 15. Distribution Function.- 16. Multivarite Distributions and Functions of Random Variables.- 17. Expectation, Variance and Moments of Higher Order.- 18. Generating Functions and Characteristic Functions.- 19. Infinitely Divisible and Stable Distributions.- 20. Conditional Distributions and Conditional Expectation.- 21. Inequalities for Random Variables.- 4. Limit Theorems.- 22. Types of Convergence for Sequences of Random Variables.- 23. Laws of Large Numbers.- 24. Central Limit Theorem and Related Topics.- Solutions, Hints, and Answers.- Table 1 (Normal distribution).- Table 2 (Poisson distribution).- References.