Synopses & Reviews
Bean's PROBABILITY: THE SCIENCE OF UNCERTAINTY WITH APPLICATIONS TO INVESTMENTS, INSURANCE, AND ENGINEERING is an 'applied' book that will be of interest to instructors teaching probability in mathematics departments of operations research, statistics, actuarial science, management science, and decision science. Comprehensive, easy to read and comprehend, and current, the book uses investment, insurance, and engineering applications throughout as a unifying theme.
Table of Contents
1. INTRODUCTION. What Is Probability? How is Uncertainty Quantified? Probability in Engineering and the Sciences. What Is Actuarial Science? What is Financial Engineering? Interpretations of Probability. Probability Modeling in Practice. Outline of This Book. Chapter Summary. Further Reading. Exercises. 2. A SURVEY OF SOME BASIC CONCEPTS THROUGH EXAMPLES. Payoff in a Simple Game. Choosing Between Payoffs. Future Lifetimes. Simple and Compound Growth. Chapter Summary. Exercises. 3. CLASSICAL PROBABILITY. The Formal Language of Classical Probability. Conditional Probability. The Law of Total Probability. Bayes Theorem. Chapter Summary. Exercises. Appendix on Sets, Combinatorics, and Basic Probability Rules. 4. RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS. Definitions and Basic Properties. Statistical Measures of Expectation, Variation and Risk. Alternative Ways of Specifying Probability Distributions. Chapter Summary. Additional Exercises. Appendix on Generalized Density Functions (Optional). 5. SPECIAL DISCRETE DISTRIBUTIONS. The Binomial Distribution. The Poisson Distribution. The Negative Binomial Distribution. The Geometric Distribution. Exercises. 6. SPECIAL CONTINUOUS DISTRIBUTIONS. Special Continuous Distributions for Modeling Uncertain Sizes. Special Continuous Distributions for Modeling Lifetimes. Other Special Distributions. Exercises. 7. TRANSFORMATIONS OF RANDOM VARIABLES. Determining the Distribution of a Transformed Random Variable. Expectation of a Transformed Random Variable. Insurance Contracts with Caps, Deductibles, and Coinsurance (Optional). Life Insurance and Annuity Contracts (Optional). Reliability of Systems with Multiple Components or Processes (Optional). Exercises. 8. SUMS AND PRODUCTS OF RANDOM VARIABLES. Techniques for Calculating the Distribution of a Sum. Distributions of Products and Quotients. Expectations of Sums and Products. The Law of Large Numbers. The Central Limit Theorem. Normal Power Approximations (Optional). Exercises. 9. MIXTURES AND COMPOUND DISTRIBUTIONS. Definitions and Basic Operations. Some Important Examples of Mixtures Arising in Insurance. Mean and Variance of a Mixture. Moment Generating Function of a Mixture. Compound Distributions. Exercises. 10. THE MARKOWITZ PORTFOLIO SELECTION MODEL. Portfolios of Two Securities. Portfolios of Two Risky Securities and a Risk-Free Asset. Portfolio Selection with Many Securities. The Capital Asset Pricing Model. Further Reading. Exercises. APPENDIXES. ANSWERS TO SELECTED EXERCISES. INDEX.