The book begins with a chapter on various finite-stage models, illustrating the wide range of applications of stochastic dynamic programming. Subsequent chapters study infinite-stage models: discounting future returns, minimizing nonnegative costs, maximizing nonnegative returns, and maximizing the long-run average return. Each of these chapters first considers whether an optimal policy need exist—providing counterexamples where appropriate—and then presents methods for obtaining such policies when they do. In addition, general areas of application are presented.
The final two chapters are concerned with more specialized models. These include stochastic scheduling models and a type of process known as a multiproject bandit. The mathematical prerequisites for this text are relatively few. No prior knowledge of dynamic programming is assumed and only a moderate familiarity with probability— including the use of conditional expectation—is necessary.
* New exercises and data examples including:
- The One-sided Chebyshev Inequality for Data
- The Logistics Distribution and Logistic Regression
- Estimation and Testing in proofreader problems
- Product Form Estimates of Life Distributions
- Observational Studies
* Updated statistical material
* New, contemporary applications
* Reflects Sheldon Ross's masterfully clear exposition
* Contains numerous examples, exercises, and homework problems
* Unique, easy-to-use software automates required computations
* Applies probability theory to everyday statistical problems and situations
* Careful development of probability, modeling, and statistical procedures leads to intuitive understanding
* Instructor's Solutions Manual is available to adopters
Real data from actual studies across life science, engineering, computing and business are incorporated in a wide variety of exercises and examples throughout the text. These examples and exercises are combined with updated problem sets and applications to connect probability theory to everyday statistical problems and situations. The book also contains end of chapter review material that highlights key ideas as well as the risks associated with practical application of the material. Furthermore, there are new additions to proofs in the estimation section as well as new coverage of Pareto and lognormal distributions, prediction intervals, use of dummy variables in multiple regression models, and testing equality of multiple population distributions.
This text is intended for upper level undergraduate and graduate students taking a course in probability and statistics for science or engineering, and for scientists, engineers, and other professionals seeking a reference of foundational content and application to these fields.Clear exposition by a renowned expert authorReal data examples that use significant real data from actual studies across life science, engineering, computing and businessEnd of Chapter review material that emphasizes key ideas as well as the risks associated with practical application of the material25% New Updated problem sets and applications, that demonstrate updated applications to engineering as well as biological, physical and computer scienceNew additions to proofs in the estimation sectionNew coverage of Pareto and lognormal distributions, prediction intervals, use of dummy variables in multiple regression models, and testing equality of multiple population distributions.
One is heuristic and nonrigorous, and attempts to develop in students an intuitive feel for the subject that enables him or her to think probabilistically. The other approach attempts a rigorous development of probability by using the tools of measure theory. The first approach is employed in this text.
The book begins by introducing basic concepts of probability theory, such as the random variable, conditional probability, and conditional expectation. This is followed by discussions of stochastic processes, including Markov chains and Poison processes. The remaining chapters cover queuing, reliability theory, Brownian motion, and simulation. Many examples are worked out throughout the text, along with exercises to be solved by students.
This book will be particularly useful to those interested in learning 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. Ideally, this text would be used in a one-year course in probability models, or a one-semester course in introductory probability theory or a course in elementary stochastic processes.
New to this Edition:
65% new chapter material including coverage of finite capacity queues, insurance risk models and Markov chainsContains compulsory material for new Exam 3 of the Society of Actuaries containing several sections in the new examsUpdated data, and a list of commonly used notations and equations, a robust ancillary package, including a ISM, SSM, and test bankIncludes SPSS PASW Modeler and SAS JMP software packages which are widely used in the field
Superior writing styleExcellent exercises and examples covering the wide breadth of coverage of probability topics Real-world applications in engineering, science, business and economics
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.Includes new section on Pareto distribution and the 80-20 rule, Benford’s law, odds, joint distribution and correlation, logistic regression, A-B testing, and examples from the world of analytics and big dataComprehensive edition that includes the most commonly used statistical software packages (SAS, SPSS, Minitab), ISM, SSM, and an online graphing calculator manual Presents a unique, historical perspective, profiling prominent statisticians and historical events to motivate learning by including interest and contextProvides exercises and examples that help guide the student towards indpendent learning using real issues and real data, e.g. stock price models, health issues, gender issues, sports, and scientific fraud
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.
New to this Edition:
-More focus on variance reduction, including control variables and their use in estimating the expected return at blackjack and their relation to regression analysis
-A chapter on Markov chain monte carlo methods with many examples
-Unique material on the alias method for generating discrete random variables
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.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.