This book covers the basic probability of distributions with an emphasis on applications from the areas of investments, insurance, and engineering. Written by a Fellow of the Casualty Actuarial Society and the Society of Actuaries with many years of experience as a university professor and industry practitioner, the book is suitable as a text for senior undergraduate and beginning graduate students in mathematics, statistics, actuarial science, finance, or engineering as well as a reference for practitioners in these fields. The book is particularly well suited for students preparing for professional exams, and for several years it has been recommended as a textbook on the syllabus of examinations for the Casualty Actuarial Society and the Society of Actuaries.
In addition to covering the standard topics and probability distributions, this book includes separate sections on more specialized topics such as mixtures and compound distributions, distributions of transformations, and the application of specialized distributions such as the Pareto, beta, and Weibull. The book also has a number of unique features such as a detailed description of the celebrated Markowitz investment portfolio selection model. A separate section contains information on how graphs of the specific distributions studied in the book can be created using MathematicaTM.
The book includes a large number of problems of varying difficulty. A student manual with solutions to selected problems is available electronically from the "Solutions Manual" link above.
An instructor''s manual for this title is available electronically. Please send email to firstname.lastname@example.org for more information.
2. A Survey of Some Basic Concepts Through Examples
3. Classical Probability
4. Random Variables and Probability Distributions
4.1 Definitions and Basic Properties
4.2 Statistical Measures of Expectation, Variation, and Risk
4.3 Alternative Ways of Specifying Probability Distributions
4.4 Chapter Summary
4.5 Additional Exercises
4.6 Appendix on Generalized Density Functions (Optional)
5. Special Discrete Distributions
6. Special Continuous Distributions
6.1 Special Continuous Distributions for Modeling
6.2 Special Continuous Distributions for Modeling Lifetimes
6.3 Other Special Distributions
7. Transformations of Random Variables
8. Sums and Products of Random Variables
8.1 Techniques for Calculating the Distribution of a Sum
8.2 Distributions of Products and Quotients
8.3 Expectations of Sums and Products
8.4 The Law of Large Numbers
8.5 The Central Limit Theorem
8.6 Normal Power Approximations (Optional)
9. Mixtures and Compound Distributions
10. The Markowitz Investment Portfolio Selection Model
Answers to Selected Exercises