Probability: The Science of Uncertainty with Applications to Investments, Insurance, and Engineering

Probability: The Science of Uncertainty with Applications to Investments, Insurance, and Engineering

by Michael A. Bean
     
 

ISBN-10: 0821847929

ISBN-13: 9780821847923

Pub. Date: 02/19/2009

Publisher: American Mathematical Society

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

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Overview

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. An instructor's manual with complete solutions to all the problems as well as supplementary material and a student manual with solutions to selected problems are available.

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Product Details

ISBN-13:
9780821847923
Publisher:
American Mathematical Society
Publication date:
02/19/2009
Series:
Pure and Applied Undergraduate Texts Series, #6
Edition description:
New Edition
Pages:
448
Product dimensions:
7.40(w) x 9.40(h) x 0.90(d)

Table of Contents

1 Introduction 1

2 A Survey of Some Basic Concepts Through Examples 19

3 Classical Probability 57

4 Random Variables and Probability Distributions 91

5 Special Discrete Distributions 186

6 Special Continuous Distributions 221

7 Transformations of Random Variables 280

8 Sums and Products of Random Variables 325

9 Mixtures and Compound Distributions 363

10 The Markowitz Investment Portfolio Selection Model 396

Appendix A The Gamma Function 421

Appendix B The Incomplete Gamma Function 423

Appendix C The Beta Function 428

Appendix D The Incomplete Beta Function 429

Appendix E The Standard Normal Distribution 430

Appendix F Mathematica Commands for Generating the Graphs of Special Distributions 432

Appendix G Elementary Financial Mathematics 434

Answers to Selected Exercises 437

Index 441

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