000			04674nam a2200181Ia 4500
020			_a9812548823
082			_a519.2 BEA
100			_aBean, Michael A
245			_aProbability: the science of uncertainty with applications to investments, insurance and engineering
250			_a-
260			_bThomson _aDelhi _c2004
300			_aXIII, 448 _b24 cm ; Pbk
500			_aRs.1140/-
505			_aTable 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 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 4.1 Definitions and Basic Properties What Is a Random Variable? What Is a Probability Distribution? Types of Distributions Probability Mass Functions Probability Density Functions Mixed Distributions Equality and Equivalence of Random Variables Random Vectors and Bivariate Distributions Dependence and Independence of Random Variables The Law of Total Probability and Bayes' Theorem (Distributional Forms) Arithmetic Operations on Random Variables The Difference Between Sums and Mixtures Exercises 4.2 Statistical Measures of Expectation, Variation, and Risk Expectation Deviation from Expectation Higher Moments Exercises 4.3 Alternative Ways of Specifying Probability Distributions Moment and Cumulant Generating Functions Survival and Hazard Functions Exercises 4.4 Chapter Summary 4.5 Additional Exercises 4.6 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 6.1 Special Continuous Distributions for Modeling Uncertain Sizes The Exponential Distribution The Gamma Distribution The Pareto Distribution 6.2 Special Continuous Distributions for Modeling Lifetimes The Weibull Distribution The DeMoivre Distribution 6.3 Other Special Distributions The Normal Distribution The Lognormal Distribution The Beta Distribution 6.4 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) Trigonometric Transformations (Optional) Exercises 8. Sums and Products of Random Variables 8.1 Techniques for Calculating the Distribution of a Sum Using the Joint Density Using the Law of Total Probability Convolutions 8.2 Distributions of Products and Quotients 8.3 Expectations of Sums and Products Formulas for the Expectation of a Sum or Product The Cauchy-Schwarz Inequality Covariance and Correlation 8.4 The Law of Large Numbers Motivating Example: Premium Determination in Insurance Statement and Proof of the Law Some Misconceptions Surrounding the Law of Large Numbers 8.5 The Central Limit Theorem 8.6 Normal Power Approximations (Optional) 8.7 Exercises 9. Mixtures and Compound Distributions Definitions and Basic Properties Some Important Examples of Mixtures Arising in Insurance Mean and Variance of a Mixture Moment Generating Function of a Mixture Compound Distributions General Formulas Special Compound Distributions Exercises 10. The Markowitz Investment 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 The Gamma Function The Incomplete Gamma Function The Beta Function The Incomplete Beta Function The Standard Normal Distribution Mathematica Commands for Generating the Graphs of Special Distributions Elementary Financial Mathematics Answers to Selected Exercises Index
650			_aMathematics ; probability
856			_uhttp://bookstore.ams.org/amstext-6
942			_cBK
999			_c101692 _d101692