Front Cover; Decation; Preface; Contents; Introduction; Chapter 1. Basic Notions; Chapter 2. Independence and Conditional Probability; Chapter 3. Discrete Random Variables; Chapter 4. Generating Functions. Branching Processes. Random Walk Revisited; Chapter 5. Markov Chains; Chapter 6. Continuous Random Variables; Chapter 7. Distributions in the General Case. Simulation; Chapter 8. Moment Generating Functions; Chapter 9. The Central Limit Theorem for Independent Random Variables; Chapter 10. Covariance Analysis. The Multivariate Normal Distribution. The Multivariate Central Limit Theorem
Chapter 11. Maxima and Minima of Random Variables. Elements of Reliability Theory. Hazard Rate and Survival ProbabilitiesChapter 12. Stochastic Processes: Preliminaries; Chapter 13. Counting and Queuing Processes. Birth and Death Processes: A General Scheme; Chapter 14. Elements of Renewal Theory; Chapter 15. Martingales in Discrete Time; Chapter 16. Brownian Motion and Martingales in Continuous Time; Chapter 17. More on Dependency Structures; Chapter 18. Comparison of Random Variables. Risk Evaluation; Appendix. Tables. Some Facts from Calculus and the Theory of Interest; References
Summary
Basic NotionsSample Space and EventsProbabilitiesCounting TechniquesIndependence and Conditional ProbabilityIndependenceConditioningThe Borel-Cantelli TheoremDiscrete Random VariablesRandom Variables and VectorsExpected ValueVariance and Other Moments. Inequalities for DeviationsSome Basic DistributionsConvergence of Random Variables. The Law of Large NumbersConditional ExpectationGenerating Functions. Branching Processes. Random Walk RevisitedBranching Processes Generating Functions Branching Processes Revisited More on Random WalkMarkov ChainsDefinitions and Examples. Probability Distributio
