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• Combinatorial analysis
• Axioms of probability
• Conditional probability and independence
• Random variables
• Continuous random variables
• Jointly distributed random variables
• Properties of expectation
• Limit theorems
• Additional topics in probability
• Simulation
• Common discrete distributions
• Common continuous distributions.

For upper-level to graduate courses in Probability or Probability and Statistics, for majors in mathematics, statistics, engineering, and the sciences. Explores both the mathematics and the many potential applications of probability theory A First Course in Probability is an elementary introduction to the theory of probability for students in mathematics, statistics, engineering, and the sciences. Through clear and intuitive explanations, it presents not only the mathematics of probability theory, but also the many diverse possible applications of this subject through numerous examples. The 10th Edition includes many new and updated problems, exercises, and text material chosen both for interest level and for use in building student intuition about probability. 0134753119 / 9780134753119 A First Course in Probability, 10/e.
(source: Nielsen Book Data)

• 1. Preface
• 2. Introduction to Statistics
• 3. Describing Data Sets Using Statistics to Summarize
• 4. Data Sets Probability
• 5. Discrete Random Variables
• 6. Normal Random Variables
• 7. Distributions of Sampling
• 8. Statistics Estimation Testing
• 9. Statistical Hypotheses
• 10. Hypothesis Tests Concerning Two Populations
• 11. Analysis of Variance Linear Regression
• 12. Chi-Squared Goodness of Fit Tests
• 13. Nonparametric Hypotheses
• 14. Tests
• 15. Quality Control
• 16. Appendices.
• (source: Nielsen Book Data)

Introductory Statistics, Fourth Edition, reviews statistical concepts and techniques in a manner that will teach students not only how and when to utilize the statistical procedures developed, but also how to understand why these procedures should be used. The text's main merits are the clarity of presentation, contemporary examples and applications from diverse areas, an explanation of intuition, and the ideas behind the statistical methods. Concepts are motivated, illustrated, and explained in a way that attempts to increase one's intuition. To quote from the preface, it is only when a student develops a feel or intuition for statistics that she or he is really on the path toward making sense of data. Ross achieves this goal through a coherent mix of mathematical analysis, intuitive discussions, and examples. Applications and examples refer to real-world issues, such as gun control, stock price models, health issues, driving age limits, school admission ages, use of helmets, sports, scientific fraud, and many others. Examples relating to data mining techniques using the number of Google queries or Twitter tweets are also considered. For this fourth edition, new topical coverage includes sections on Pareto distribution and the 80-20 rule, Benford's law, added material on odds and joint distributions and correlation, logistic regression, A-B testing, and more modern (big data) examples and exercises.
(source: Nielsen Book Data)

Sheldon Ross's classic bestseller, Introduction to Probability Models, has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. It introduces elementary probability theory and stochastic processes, and shows how probability theory can be applied fields such as engineering, computer science, management science, the physical and social sciences, and operations research. The hallmark features of this renowned text remain in this eleventh edition: superior writing style; excellent exercises and examples covering the wide breadth of coverage of probability topic; and real-world applications in engineering, science, business and economics. The 65% new chapter material includes coverage of finite capacity queues, insurance risk models, and Markov chains, as well as updated data. * Updated data, and a list of commonly used notations and equations, instructor's solutions manual* Offers new applications of probability models in biology and new material on Point Processes, including the Hawkes process* Introduces elementary probability theory and stochastic processes, and shows how probability theory can be applied in fields such as engineering, computer science, management science, the physical and social sciences, and operations research* Covers finite capacity queues, insurance risk models, and Markov chains * Contains compulsory material for new Exam 3 of the Society of Actuaries including several sections in the new exams* Appropriate for a full year course, this book is written under the assumption that students are familiar with calculus.
(source: Nielsen Book Data)

• 1. Combinatorial Analysis
• 2. Axioms of Probability
• 3. Conditional Probability and Independence
• 4. Random Variables
• 5. Continuous Random Variables
• 6. Jointly Distributed Random Variables
• 7. Properties of Expectation
• 8. Limit Theorems
• 9. Additional Topics in Probability
• 10. Simulation Appendix A. Answers to Selected Problems Appendix B. Solutions to Self-Test Problems and Exercises Index.
• (source: Nielsen Book Data)

A First Course in Probability, Eighth Edition, features clear and intuitive explanations of the mathematics of probability theory, outstanding problem sets, and a variety of diverse examples and applications. This book is ideal for an upper-level undergraduate or graduate level introduction to probability for math, science, engineering and business students. It assumes a background in elementary calculus.
(source: Nielsen Book Data)

Ross' classic bestseller, "Introduction to Probability Models", has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. It provides an introduction to elementary probability theory and stochastic processes, and shows how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries. New to this Edition are 65 per cent new chapter material including coverage of finite capacity queues, insurance risk models and Markov chains. It contains compulsory material for new Exam 3 of the Society of Actuaries containing several sections in the new exams. It has updated data, and a list of commonly used notations and equations, a robust ancillary package, including a ISM, SSM, test bank, and companion website. it includes SPSS PASW Modeler and SAS JMP software packages which are widely used in the field. Hallmark features: superior writing style; excellent exercises and examples covering the wide breadth of coverage of probability topics; and real-world applications in engineering, science, business and economics.
(source: Nielsen Book Data)

This updated text provides a superior introduction to applied probability and statistics for engineering or science majors. It emphasizes the manner in which probability yields insight into statistical problems; ultimately resulting in an intuitive understanding of the statistical procedures most often used by practicing engineers and scientists. Real data sets are incorporated in a wide variety of exercises and examples throughout the book, and this emphasis on data motivates the probability coverage. As with the previous editions, this text has tremendously clear exposition, plus real-data examples and exercises throughout the text. Numerous exercises, examples, and applications apply probability theory to everyday statistical problems and situations. New to the 4th Edition: new chapter on Simulation, Bootstrap Statistical Methods, and Permutation Tests; 20% new updated problem sets and applications, that demonstrate updated applications to engineering as well as biological, physical and computer science; new real data examples that use significant real data from actual studies across life science, engineering, computing and business; and, new end of chapter review material that emphasizes key ideas as well as the risks associated with practical application of the material.
(source: Nielsen Book Data)

• Preface
• 1. Introduction to Probability Theory--
• 2. Random Variables
• 3. Conditional Probability and Conditional Expectation
• 4. Markov Chains
• 5. The Exponential Distribution and the Poisson Process
• 6. Continuous-Time Markov Chains
• 7. Renewal Theory and Its Applications
• 8. Queueing Theory
• 9. Reliability Theory
• 10. Brownian Motion and Stationary Processes
• 11. Simulation Appendix: Solutions to Starred Exercises Index.
• (source: Nielsen Book Data)

Introduction to Probability Models, Ninth Edition, is the primary text for a first undergraduate course in applied probability. This updated edition of Ross's classic bestseller provides an introduction to elementary probability theory and stochastic processes, and shows how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries. This book now contains a new section on compound random variables that can be used to establish a recursive formula for computing probability mass functions for a variety of common compounding distributions; a new section on hiddden Markov chains, including the forward and backward approaches for computing the joint probability mass function of the signals, as well as the Viterbi algorithm for determining the most likely sequence of states; and a simplified approach for analyzing nonhomogeneous Poisson processes. There are also additional results on queues relating to the conditional distribution of the number found by an M/M/1 arrival who spends a time t in the system; inspection paradox for M/M/1 queues; and M/G/1 queue with server breakdown. Furthermore, the book includes new examples and exercises, along with compulsory material for new Exam 3 of the Society of Actuaries. This book is essential reading for professionals and students in actuarial science, engineering, operations research, and other fields in applied probability.
(source: Nielsen Book Data)
Ross's classic bestseller, Introduction to Probability Models, has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. It provides an introduction to elementary probability theory and stochastic processes, and shows how probability theory can be applied to the study of phenomena in fields such as engineering, computer science, management science, the physical and social sciences, and operations research. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries. A new section (3.7) on COMPOUND RANDOM VARIABLES, that can be used to establish a recursive formula for computing probability mass functions for a variety of common compounding distributions. A new section (4.11) on HIDDDEN MARKOV CHAINS, including the forward and backward approaches for computing the joint probability mass function of the signals, as well as the Viterbi algorithm for determining the most likely sequence of states. Simplified Approach for Analyzing Nonhomogeneous Poisson processes Additional results on queues relating to the (a) conditional distribution of the number found by an M/M/1 arrival who spends a time t in the system; (b) inspection paradox for M/M/1 queues (c) M/G/1 queue with server breakdown Many new examples and exercises.
(source: Nielsen Book Data)

• 1. Measure Theory and Laws of Large Numbers
• Introduction
• A Non-Measurable Event
• Countable and Uncountable Sets
• Probability Spaces
• Random Variables
• Expected Value
• Almost Sure Convergence and the Dominated Convergence Theorem
• Convergence in Probablitiy and in Distribution
• Law of Large Numbers and Ergodic Theorem
• Exercises
• 2. Stein's Method and Central Limit Theorems
• Introduction
• Coupling
• Poisson Approximation and Le Cam's Theorem
• The Stein-Chen Method
• Stein's Method for the Geometric Distribution
• Stein's Method for the Normal Distribution
• Exercises
• 3. Conditional Expectation and Martingales
• Introduction
• Conditional Expectation
• Martingales
• The Martingale Stopping Theorem
• The Hoeffding-Azuma Inequality
• Submartingales, Supermartingales, and a Convergence Theorem
• Exercises
• 4. Bounding Probabilities and Expectations
• Introduction
• Jensen's Inequality
• Probability Bounds via the Importance Sampling Identity
• Chernoff Bounds
• Second Moment and Conditional Expectation Inequalities
• The Min-Max Identity and Bounds on the Maximum
• Stochastic Orderings
• Exercises
• 5. Markov Chains
• Introduction
• The Transition Matrix
• The Strong Markov Property
• Classification of States
• Stationary and Limiting Distributions
• Time Reversibility
• A Mean Passage Time Bound
• Exercises
• 6. Renewal Theory
• Introduction
• Some Limit Theorems of Renewal Theory
• Renewal Reward Processes
• 6.3.1 Queueing Theory Applications of Renewal Reward Processes
• Blackwell's Theorem
• The Poisson Process
• Exercises
• 7. Brownian Motion
• Introduction
• Continuous Time Martingales
• Construction Brownian Motion
• Embedding Variables in Brownian Motion
• The Central Limit Theorem
• Exercises.

• 1. Combinatorial Analysis.
• 2. Axioms of Probability.
• 3. Conditional Probability and Independence.
• 4. Random Variables.
• 5. Continuous Random Variables.
• 6. Jointly Distributed Random Variables.
• 7. Properties of Expectation.
• 8. Limit Theorems.
• 9. Additional Topics in Probability.
• 10. Simulation. Appendix A. Answers to Selected Problems. Appendix B. Solutions to Self-Test Problems and Exercises. Index.
• (source: Nielsen Book Data)

For upper-level or undergraduate/graduate level introduction to probability for math, science, engineering, and business students with a background in elementary calculus. This highly successful text is written as an elementary introduction to the mathematical theory of probability for students in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus.
(source: Nielsen Book Data)

• Preface-- Introduction-- Elements of Probability-- Random Numbers-- Generating Discrete Random Variables-- Generating Continuous Random Variables-- The Discrete Event Simulation Approach-- Statistical Analysis of Simulated Data-- Variance Reduction Techniques-- Statistical Validation Techniques-- Markov Chain Monte Carlo Methods-- Some Additional Topics-- Exercises-- References-- Index.
• (source: Nielsen Book Data)

Ross's Simulation, Fourth 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 text explains how a computer can be used to generate random numbers, and how to use these random numbers to generate the behavior of a stochastic model over time. It presents the statistics needed to analyze simulated data as well as that needed for validating the simulation model.
(source: Nielsen Book Data)

• (NOTE: Each chapter concludes with Summary, Problems, Theoretical Exercises, and Self-Test Problems and Exercises.)
• 1. Combinatorial Analysis. Introduction. The Basic Principle of Counting. Permutations. Combinations. Multinomial Coefficients. The Number of Integer Solutions of Equations.
• 2. Axioms of Probability. Introduction. Sample Space and Events. Axioms of Probability. Some Simple Propositions. Sample Spaces Having Equally Likely Outcomes. Probability As a Continuous Set Function. Probability As a Measure of Belief.
• 3. Conditional Probability and Independence. Introduction. Conditional Probabilities. Bayes' Formula. Independent Events. P(*
• (source: Nielsen Book Data)

For upper level or undergraduate/graduate level introduction to probability for math, science, engineering, and business students with a background in elementary calculus.This market-leading introduction to probability features exceptionally clear explanations of the mathematics of probability theory and explores its many diverse applications through numerous interesting and motivational examples. The outstanding problem sets and intuitive explanations are hallmark features of this market leading text.
(source: Nielsen Book Data)

• Preface-- Introduction-- Elements of Probability-- Random Numbers-- Generating Discrete Random Variables-- Generating Continuous Random Variables-- The Discrete Event Simulation Approach-- Statistical Analysis of Simulated Data-- Variance Reduction Techniques-- Statistical Validation Techniques-- Markov Chain Monte Carlo Methods-- Some Additional Topics-- Exercises-- References-- Index.
• (source: Nielsen Book Data)

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.
(source: Nielsen Book Data)

• *Combinatorial Analysis *Axioms of Probability *Conditional Probability and Independence *Random Variables *Continuous Random Variables *Jointly Distributed Random Variables *Properties of Expectation *Limit Theorems *Additional Topics in Probability *Simulation *Appendix A. Answers to Selected Problems *Appendix B. Solutions to Self-Test Problems and Exercises *Index.
• (source: Nielsen Book Data)

This market leader is written as an elementary introduction to the mathematical theory of probability for students in mathematics, engineering, and the sciences who possess the prerequisite knowledge of elementary calculus. A major thrust of the Fifth Edition has been to make the book more accessible to today's students. The exercise sets have been revised to include more simple, mechanical problems and a new section of Self-Test Problems with fully worked out solutions conclude each chapter. In addition, many new applications have been added to demonstrate the importance of probability in real situations. A software diskette, referenced in text and packaged with each copy of the book, provides an easy to use tool for students to derive probabilities for binomial, Poisson, and normal random variables, illustrate and explore the central limit theorem, work with the strong law of large numbers, and more.
(source: Nielsen Book Data)

• Part 1 Elements of probability: sample space and events-- axioms of probability-- conditional probability and independence-- random variables-- expectation-- variance-- Chebyshev's inequality and the laws of large numbers-- some discrete random variables-- continuous random variables-- conditional expectation and conditional variance problems.
• Part 2 Random numbers: pseudo-random number generation-- using random numbers to evaluate integrals.
• Part 3 Generating discrete random variables: the inverse transform method-- generating a Poisson random variable-- generating binomial random variables-- the acceptance-rejection technique-- the composition approach.
• Part 4 Generating continuous random variables: the inverse transform algorithm-- the rejection method-- the polar method for generating normal random variables-- generating a Poisson process-- generating a non-homogeneous Poisson process.
• Part 5 The discrete event simulation approach: simulation via discrete events-- a single server queueing system-- a queueing system with two servers in series-- a queueing system with two parallel servers-- an inventory model-- a repair problem-- exercising a stock option-- verification of the simulation model problems.
• Part 6 Statistical analysis of simulated data: the sample means and sample variance-- interval estimates of a population mean-- the bootstrapping technique for estimating mean square errors.
• Part 7 Variance reduction techniques: the use of antipathetic variables-- the use of control variates-- variance reduction by conditioning-- stratified sampling-- importance sampling-- using common random numbers.
• Part 8 Statistical validation techniques: goodness of fit tests-- goodness of fit tests when some parameters are unspecified-- the two-sample problem-- validating the assumption of a nonhomogeneous Poisson process.
• Part 9 Markov chain Monte Carlo methods: Markov chains-- the Hastings-Metropolis algorithm-- the Gibbs sampler-- simulated annealing-- the sampling importance-- resampling algorithm.
• Part 10 Some additional topics: the alias method for generating discrete random variables-- simulating a two-dimensional Poisson process-- simulation applications of an identity for sums of Bernoulli random variables-- estimating probabilities and expected first passage times by using random hazards-- appendix.
• (source: Nielsen Book Data)

Simulation allows complex real world situations to be analyzed quantitatively. First, a model is created to represent the situation, then, using probability and statistics theory, the computer can perform a simulation to predict the outcome of this situation. This text provides a description of the generation of random variables and their use in analyzing a model in simulation study. It details how a computer may be used to generate random numbers, which may then be used to generate the behaviour of a stochastic model over time. The statistics needed to analyze simulated data and to validate the simulation model are also presented.
(source: Nielsen Book Data)

• Preliminaries. The Poisson Process. Renewal Theory. Markov Chains. Continuous--Time Markov Chains. Martingales. Random Walks. Brownian Motion and Other Markov Processes. Stochastic Order Relations. Poisson Approximations. Answers and Solutions to Selected Problems. Index.
• (source: Nielsen Book Data)

A nonmeasure theoretic introduction to stochastic processes. Considers its diverse range of applications and provides readers with probabilistic intuition and insight in thinking about problems. This revised edition contains additional material on compound Poisson random variables including an identity which can be used to efficiently compute moments; a new chapter on Poisson approximations; and coverage of the mean time spent in transient states as well as examples relating to the Gibb's sampler, the Metropolis algorithm and mean cover time in star graphs. Numerous exercises and problems have been added throughout the text.
(source: Nielsen Book Data)

• Elements of Probability. Random Variables and Expectation. Special Random Variables. Sampling. Parameter Estimation. Hypothesis Testing. Regression. Analysis of Variance. Goodness of Fit and Nonparametric Testing. Life Testing. Quality Control. Simulation. Appendix of Programs. Appendix of Tables. Index.
• (source: Nielsen Book Data)

A comprehensive introductory text providing a clear treatment of the fundamental concepts and applications of probability and statistics. After a general overview of the subject, it considers special types of random variables using several examples which illustrate their wide variety of applications. The book also examines their calculation and presents computer programs that calculate the probability distribution and their inverse of binomial, poisson, normal, t, F and Chi-square distributions. Its coverage on sampling thoroughly reviews such topics as the sample mean, sample variance, sample median, as well as histograms, empirical distribution functions and stem- and-leaf plots; a program for computing sample mean and sample variance for a given data set is included. Among the other topics discussed in this work are hypothesis testing; regression, both simple and linear; and problems related to life testing. Also included is a diskette of 35 programs for the IBM PC, giving exact answers or approximations where appropriate.
(source: Nielsen Book Data)