Sheldon Ross' Simulation, Third Edition introduces aspiring and practicing actuaries, engineers, computer scientists and others to the practical aspects of constructing computerized simulation studies to analyze and interpret real phenomena. Readers learn to apply results of these analyses to problems in a wide variety of fields to obtain effective, accurate solutions and make predictions about future outcomes. This new edition provides a comprehensive, in-depth, and current guide for constructing probability models and simulations for a variety of purposes. It features new information, including the presentation of the Insurance Risk Model, generating a Random Vector, and evaluating an Exotic Option. Also new is coverage of the changing nature of statistical methods due to the advancements in computing technology. Table of Contents   Preface 1. Introduction Exercises 2. Elements of Probability 2.1 Sample Space and Events 2.2 Axioms of Probability 2.3 Conditional Probability and Independence 2.4 Random Variables 2.5 Expectation 2.6 Variance 2.7 Chebyshev's Inequality and the Laws of Large Numbers 2.8 Some Discrete Random Variables Binomial Random Variables Poisson Random Variables Geometric Random Variables The Negative Binomial Random Variable Hypergeometric Random Variables 2.9 Continuous Random Variables Uniformly Distributed Random Variables Normal Random Variables Exponential Random Variables The Poisson Process and Gamma Random Variables The Nonhomogeneous Poisson Process 2.10 Conditional Expectation and Conditional Variance Exercises References 3. Random Numbers Introduction 3.1 Pseudorandom Number Generation 3.2 Using Random Numbers to Evaluate Integrals Exercises References 4. Generating Discrete Random Variables 4.1 The Inverse Transform Method 4.2 Generating a Poisson Random Variable 4.3 Generating Binomial Random Variables 4.4 The Acceptance-Rejection Technique 4.5 The Composition Approach 4.6 Generating Random Vectors Exercises 5. Generating Continuous Random Variables Introduction 5.1 The Inverse Transform Algorithm 5.2 The Rejection Method 5.3 The Polar Method for Generating Normal Random Variables 5.4 Generating a Poisson Process 5.5 Generating a Nonhomogeneous Poisson Process Exercises References 6. The Discrete Event Simulation Approach Introduction 6.1 Simulation via Discrete Events 6.2 A Single-Server Queueing System 6.3 A Queueing System with Two Servers in Series 6.4 A Queueing System with Two Parallel Servers 6.5 An Inventory Model 6.6 An Insurance Risk Model 6.7 A Repair Problem 6.8 Exercising a Stock Option 6.9 Verification of the Simulation Model Exercises References 7. Statistical Analysis of Simulated Data Introduction 7.1 The Sample Mean and Sample Variance 7.2 Interval Estimates of a Population Mean 7.3 The Bootstrapping Technique for Estimating MeanSquare Errors Exercises References 8. Variance Reduction Techniques Introduction 8.1 The Use of Antithetic Variables 8.2 The Use of Control Variates 8.3 Variance Reduction by Conditioning Estimating the Expected Number of Renewals by Time A 8.4 Stratified Sampling 8.5 Importance Sampling 8.6 Using Common Random Numbers 8.7 Evaluating an Exotic Option Appendix: Verification of Antithetic Variable ApproachWhen Estimating the Expected Value of Monotone Functions Exercises References 9. Statistical Validation Techniques Introduction 9.1 Goodness of Fit Tests The Chi-Square Goodness of Fit Test for Discrete Data The Kolmogorov-Smirnov Test for Continuous Data 9.2 Goodness of Fit Tests When Some Parameters Are Unspecified The Discrete Data Case The Continuous Data Case 9.3 The Two-Sample Problem 9.4 Validating the Assumption of a NonhomogeneousPoisson Process Exercises References 10. Markov Chain Monte Carlo Methods Introduction 10.1 Markov Chains 10.2 The Hastings-Metropolis Algorithm 10.3 The Gibbs Sampler 10.4 Simulated Annealing 10.5 The Sampling Importance Resampling Algorithm Exercises References 11. Some Additional Topics Introduction 11.1 The Alias Method for Generating DiscreteRandom Variables 11.2 Simulating a Two-Dimensional Poisson Process 11.3 Simulation Applications of an Identity for Sums of BernoulliRandom Variables 11.4 Estimating the Distribution and the Mean of the First PassageTime of a Markov Chain 11.5 Coupling from the Past Exercises References Index