Author | Haigh, John. author |
---|---|
Title | Probability Models [electronic resource] / by John Haigh |
Imprint | London : Springer London : Imprint: Springer, 2002 |
Connect to | http://dx.doi.org/10.1007/978-1-4471-0169-7 |
Descript | VIII, 256 p. online resource |
1. Probability Spaces -- 1.1 Introduction -- 1.2 The Idea of Probability -- 1.3 Laws of Probability -- 1.4 Consequences -- 1.5 Equally Likely Outcomes -- 1.6 The Continuous Version -- 1.7 Intellectual Honesty -- 2. Conditional Probability and Independence -- 2.1 Conditional Probability -- 2.2 Bayesโ Theorem -- 2.3 Independence -- 2.4 The Borel-Cantelli Lemmas -- 3. Common Probability Distributions -- 3.1 Common Discrete Probability Spaces -- 3.2 Probability Generating Functions -- 3.3 Common Continuous Probability Spaces -- 3.4 Mixed Probability Spaces -- 4. Random Variables -- 4.1 The Definition -- 4.2 Discrete Random Variables -- 4.3 Continuous Random Variables -- 4.4 Jointly Distributed Random Variables -- 4.5 Conditional Expectation -- 5. Sums of Random Variables -- 5.1 Discrete Variables -- 5.2 General Random Variables -- 5.3 Records -- 6. Convergence and Limit Theorems -- 6.1 Inequalities -- 6.2 Convergence -- 6.3 Limit Theorems -- 6.4 Summary -- 7. Stochastic Processes in Discrete Time -- 7.1 Branching Processes -- 7.2 Random Walks -- 7.3 Markov Chains -- 8. Stochastic Processes in Continuous Time -- 8.1 Markov Chains in Continuous Time -- 8.2 Queues -- 8.3 Renewal Theory -- 8.4 Brownian Motion: The Wiener Process -- 9. Appendix: Common Distributions and Mathematical Facts -- 9.1 Discrete Distributions -- 9.2 Continuous Distributions -- 9.3 Miscellaneous Mathematical Facts -- Solutions