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Probability and Stochastic Modeling

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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 Read more...

Abstract: 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

Author(s): Rotar, Vladimir I
Publisher: CRC Press
Year: 2012

Language: English
Pages: 504
City: Hoboken
Tags: Математика;Теория вероятностей и математическая статистика;Теория вероятностей;

Content: 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