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Preface.
To the Student.
To the Instructor.
Coverage.
Acknowledgments.
Chapter 1. Modeling.
1.1 Choice and Chance.
1.2 The Model Building Process.
1.3 Modeling in the Mathematical Sciences.
1.4 A First Look at a Probability Model: The Random Walk.
1.5 Brief Applications of Random Walks.
Exercises.
Chapter 2. Sets and Functions.
2.1 Operations with Sets.
2.2 Functions.
2.3 The Probability Function and the Axioms of Probability.
2.4 Equally Likely Sample Spaces and Counting Rules.
Rules.
Exercises.
Chapter 3. Probility Laws I: Building on the Axioms.
3.1 The Complement Rule.
3.2 The Addition Rule.
3.3 Extensions and Additional Results.
Exercises.
Chapter 4. Probility Laws II: Results of Conditioning.
4.1 Conditional Probability and the Multiplication Rule.
4.2 Independent Events.
4.3 The Theorem of Total Probabilities and Bayes' Rule.
4.4 Problems of Special Interest: Effortful Illustrations of the Probability Laws.
Exercises.
Chapter 5. Random Variables and Stochastic Processes.
5.1 Roles and Types of Random Variables.
5.2 Expectation.
5.3 Roles, Types, and Characteristics of Stochastic Processes.
Exercises.
Chapter 6. Discrete Random Variables and Applications in Stochastic Processes.
6.1 The Bernoulli and Binomial Models.
6.2 The Hypergeometric Model.
6.3 The Poisson Model.
6.4 The Geometric and Negative Binomial.
Models.
Exercises.
Chapter 7. Continuous Random Variables and Applications in Stochastic Processes.
7.1 The Continuous Uniform Model.
7.2 The Exponential Model.
7.3 The Gamma Model.
7.4 The Normal Model.
Chapter 8. Covariance and Correlation Among Random Variables.
8.1 Joint, Marginal and Conditional Distributions.
8.2 Covariance and Correlation.
8.3 Brief Examples and Illustrations in Stochastic Processes and Times Series.
Exercises.
Bibliography.
Tables.
Index.
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Add Probability : Modeling and Applications to Random Processes, Improve Your Probability of Mastering This Topic This book takes an innovative approach to calculus-based probability theory, considering it within a framework for creating models of random phenomena. The author focuses on the synthesis of stochastic m, Probability : Modeling and Applications to Random Processes to the inventory that you are selling on WonderClubX
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Add Probability : Modeling and Applications to Random Processes, Improve Your Probability of Mastering This Topic This book takes an innovative approach to calculus-based probability theory, considering it within a framework for creating models of random phenomena. The author focuses on the synthesis of stochastic m, Probability : Modeling and Applications to Random Processes to your collection on WonderClub |