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Probability is presented in a very clear way in this text: through interesting and instructive examples and exercises that motivate the theory, definitions, theorems, and methodology. Due to its unique organization, this text has also been successfully used in teaching courses in discrete probability. Salient Features • NEW - Chapter on Stochastic Processes-Covers more in-depth material on Poisson processes, presents the basics of Markov chains, continuous-time Markov chains, and Brownian Motion. This text is now the most comprehensive available in probability • NEW - Applications of probability and stochastic processes in finance-Includes some practical, meaningful, non-trivial, and relevant applications of probability and stochastic processes in finance, economics, and actuarial sciences • NEW - Comprehensive new section on applications to Genetics-Covers basic concepts of genetics including many important examples throughout the book • NEW - New section on Survival Analysis and Hazard Functions • NEW - Fine-tuned for accuracy-Praised for being very accurate and virtually error free • NEW - More explanations and clarifying comments. • NEW - 276 new exercises and examples-Adds new application problems • NEW - More insightful and better solutions • Historical roots and applications of many of the theorems and definitions • Simple probabilistic arguments-Given with the usual analytic proofs Table of Content 1. Axioms of Probability. 2. Combinatorial Methods. 3. Conditional Probability and Independence. 4. Distribution Functions and Discrete Random Variables. 5. Special Discrete Distributions. 6. Continuous Random Variables. 7. Special Continuous Distributions. 8. Bivariate Distributions. 9. Multivariate Distributions. 10. More Expectations and Variances. 11. Sums of Independent Random Variables and Limit Theorems. 12. Stochastic Processes. 13. Simulation. Answers to Odd-Numbered Exercises. ISBN - 9789332535107
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