Author | Stoyanov, J. author |
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Title | Exercise Manual in Probability Theory [electronic resource] / by J. Stoyanov, I. Mirazchiiski, Z. Ignatov, M. Tanushev |
Imprint | Dordrecht : Springer Netherlands : Imprint: Springer, 1989 |
Connect to | http://dx.doi.org/10.1007/978-94-009-2927-2 |
Descript | XII, 352 p. online resource |
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. Bayesโ 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