# Student Solutions Manual to Accompany Simulation and the Monte Carlo Method / Edition 2

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### Overview

This accessible new edition explores the major topics in Monte Carlo simulation

Simulation and the Monte Carlo Method, Second Edition reflects the latest developments in the field and presents a fully updated and comprehensive account of the major topics that have emerged in Monte Carlo simulation since the publication of the classic First Edition over twenty-five years ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences.

The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including:

Markov Chain Monte Carlo

Variance reduction techniques such as the transform likelihood ratio method and the screening method

The score function method for sensitivity analysis

The stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization

The cross-entropy method to rare events estimation and combinatorial optimization

Application of Monte Carlo techniques for counting problems, with an emphasis on the parametric minimum cross-entropy method

An extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly for advanced readers. A generous sampling of applied examples is positioned throughout the book, emphasizing various areas of application, and a detailed appendix presents an introduction to exponential families, a discussion of the computational complexity of stochastic programming problems, and sample MATLABĀ® programs.

Requiring only a basic, introductory knowledge of probability and statistics, Simulation and the Monte Carlo Method, Second Edition is an excellent text for upper-undergraduate and beginning graduate courses in simulation and Monte Carlo techniques. The book also serves as a valuable reference for professionals who would like to achieve a more formal understanding of the Monte Carlo method.

### Meet the Author

Reuven Y. Rubinstein, DSc, is Professor Emeritus in the Faculty of Industrial Engineering and Management at Technion-Israel Institute of Technology. He has served as a consultant at numerous large-scale organizations, such as IBM, Motorola, and NEC. The author of over 100 articles and six books, Dr. Rubinstein is also the inventor of the popular score-function method in simulation analysis and generic cross-entropy methods for combinatorial optimization and counting.

Dirk P. Kroese, PhD, is Senior Lecturer in Statistics in the Department of Mathematics at The University of Queensland, Australia. He has published over fifty articles in a wide range of areas in applied probability and statistics, including Monte Carlo methods, cross-entropy, randomized algorithms, tele-traffic theory, reliability, computational statistics, applied probability, and stochastic modeling.

Preface.

Acknolwedgments.

I: Problems.

1. Preliminaries.

2. Random Number, random Variable, and Stochastic Process Generation.

3. Simulatin of Discrete-Event Systems.

4. Stastical Analysis of Discrete-Event Systems.

5. Controlling the Variance.

6. Markov Chain Monte Carlo.

7. Sensitivity Analysis and Monte Carlo Optimization.

8. The Cross-Entropy Method.

9. Counting via Monte Carlo.

10. Appendix.

II: Solutions.

11. Prelimiaries.

12. Random Number, Random Variable, and Stochastic Process Generation.

13. Simulatin of Discrete-Event Systems.

14. Stastical Analysis of Discrete-Event Systems.

15. Controlling the Variance.

16. Markov Chain Monte Carlo.

17. Sensitivity Analysis and Monte Carlo Optimization.

18. The Cross-Entropy Method.

19. Counting via Monte Carlo.

20. Appendix.

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