Advertisement
| understanding probability henk tijms: Understanding Probability Henk Tijms, 2012-06-14 Using everyday examples to demystify probability, this classic is now in its third edition with new chapters, exercises and examples. |
| understanding probability henk tijms: Understanding Probability Henk Tijms, 2007-07-26 In this fully revised second edition of Understanding Probability, the reader can learn about the world of probability in an informal way. The author demystifies the law of large numbers, betting systems, random walks, the bootstrap, rare events, the central limit theorem, the Bayesian approach and more. This second edition has wider coverage, more explanations and examples and exercises, and a new chapter introducing Markov chains, making it a great choice for a first probability course. But its easy-going style makes it just as valuable if you want to learn about the subject on your own, and high school algebra is really all the mathematical background you need. |
| understanding probability henk tijms: Understanding Probability H. C. Tijms, 2004-08-16 Like it or not, chance plays a big part in our lives. Every day we face situations where the result is uncertain, and, perhaps without realizing it, we guess about the likelihood of one outcome or another. Fortunately, mastering the concepts of probability can cast new light on situations where randomness and chance appear to rule. In this book, which uses lotteries and casino games to provide the many illustrative examples, the reader can learn about the world of probability. The author demystifies the law of large numbers, betting systems, random walks, the bootstrap, rare events, the central limit theorem, the Bayesian approach and more. Written with wit and clarity, this book can be read easily by anyone who is not put off by a few numbers and some high-school algebra. It is also ideally suited to students of all disciplines taking their first course in probability. |
| understanding probability henk tijms: Basic Probability: What Every Math Student Should Know (Second Edition) Henk Tijms, 2021-07-07 The second edition represents an ongoing effort to make probability accessible to students in a wide range of fields such as mathematics, statistics and data science, engineering, computer science, and business analytics. The book is written for those learning about probability for the first time. Revised and updated, the book is aimed specifically at statistics and data science students who need a solid introduction to the basics of probability.While retaining its focus on basic probability, including Bayesian probability and the interface between probability and computer simulation, this edition's significant revisions are as follows:The approach followed in the book is to develop probabilistic intuition before diving into details. The best way to learn probability is by practising on a lot of problems. Many instructive problems together with problem-solving strategies are given. Answers to all problems and worked-out solutions to selected problems are also provided.Henk Tijms is the author of several textbooks in the area of applied probability. In 2008, he had received the prestigious INFORMS Expository Writing Award for his work. He is active in popularizing probability at Dutch high schools. |
| understanding probability henk tijms: A First Course in Stochastic Models Henk C. Tijms, 2003-07-22 The field of applied probability has changed profoundly in the past twenty years. The development of computational methods has greatly contributed to a better understanding of the theory. A First Course in Stochastic Models provides a self-contained introduction to the theory and applications of stochastic models. Emphasis is placed on establishing the theoretical foundations of the subject, thereby providing a framework in which the applications can be understood. Without this solid basis in theory no applications can be solved. Provides an introduction to the use of stochastic models through an integrated presentation of theory, algorithms and applications. Incorporates recent developments in computational probability. Includes a wide range of examples that illustrate the models and make the methods of solution clear. Features an abundance of motivating exercises that help the student learn how to apply the theory. Accessible to anyone with a basic knowledge of probability. A First Course in Stochastic Models is suitable for senior undergraduate and graduate students from computer science, engineering, statistics, operations resear ch, and any other discipline where stochastic modelling takes place. It stands out amongst other textbooks on the subject because of its integrated presentation of theory, algorithms and applications. |
| understanding probability henk tijms: An Introduction to Probability Theory and Its Applications, Volume 1 William Feller, 1968-01-15 The nature of probability theory. The sample space. Elements of combinatorial analysis. Fluctuations in coin tossing and random walks. Combination of events. Conditional probability, stochastic independence. The binomial and the Poisson distributions. The Normal approximation to the binomial distribution. Unlimited sequences of Bernoulli trials. Random variables, expectation. Laws of large numbers. Integral valued variables, generating functions. Compound distributions. Branching processes. Recurrent events. Renewal theory. Random walk and ruin problems. Markov chains. Algebraic treatment of finite Markov chains. The simplest time-dependent stochastic processes. Answer to problems. Index. |
| understanding probability henk tijms: Probability-Based Structural Fire Load Leo Razdolsky, 2014-08-25 This book introduces the subject of probabilistic analysis to engineers and can be used as a reference in applying this technology. |
| understanding probability henk tijms: Probability, Random Processes, and Statistical Analysis Hisashi Kobayashi, Brian L. Mark, William Turin, 2011-12-15 Together with the fundamentals of probability, random processes and statistical analysis, this insightful book also presents a broad range of advanced topics and applications. There is extensive coverage of Bayesian vs. frequentist statistics, time series and spectral representation, inequalities, bound and approximation, maximum-likelihood estimation and the expectation-maximization (EM) algorithm, geometric Brownian motion and Itô process. Applications such as hidden Markov models (HMM), the Viterbi, BCJR, and Baum–Welch algorithms, algorithms for machine learning, Wiener and Kalman filters, and queueing and loss networks are treated in detail. The book will be useful to students and researchers in such areas as communications, signal processing, networks, machine learning, bioinformatics, econometrics and mathematical finance. With a solutions manual, lecture slides, supplementary materials and MATLAB programs all available online, it is ideal for classroom teaching as well as a valuable reference for professionals. |
| understanding probability henk tijms: Probability and Stochastic Processes Roy D. Yates, David J. Goodman, 2014-01-28 This text introduces engineering students to probability theory and stochastic processes. Along with thorough mathematical development of the subject, the book presents intuitive explanations of key points in order to give students the insights they need to apply math to practical engineering problems. The first five chapters contain the core material that is essential to any introductory course. In one-semester undergraduate courses, instructors can select material from the remaining chapters to meet their individual goals. Graduate courses can cover all chapters in one semester. |
| understanding probability henk tijms: Computation and Modelling in Insurance and Finance Erik Bølviken, 2014-04-10 This practical introduction outlines methods for analysing actuarial and financial risk at a fairly elementary mathematical level suitable for graduate students, actuaries and other analysts in the industry who could use simulation as a problem solver. Numerous exercises with R-code illustrate the text. |
| understanding probability henk tijms: Modern Statistics for Modern Biology SUSAN. HUBER HOLMES (WOLFGANG.), Wolfgang Huber, 2018 |
| understanding probability henk tijms: Introduction to Stochastic Processes with R Robert P. Dobrow, 2016-03-07 An introduction to stochastic processes through the use of R Introduction to Stochastic Processes with R is an accessible and well-balanced presentation of the theory of stochastic processes, with an emphasis on real-world applications of probability theory in the natural and social sciences. The use of simulation, by means of the popular statistical software R, makes theoretical results come alive with practical, hands-on demonstrations. Written by a highly-qualified expert in the field, the author presents numerous examples from a wide array of disciplines, which are used to illustrate concepts and highlight computational and theoretical results. Developing readers’ problem-solving skills and mathematical maturity, Introduction to Stochastic Processes with R features: More than 200 examples and 600 end-of-chapter exercises A tutorial for getting started with R, and appendices that contain review material in probability and matrix algebra Discussions of many timely and stimulating topics including Markov chain Monte Carlo, random walk on graphs, card shuffling, Black–Scholes options pricing, applications in biology and genetics, cryptography, martingales, and stochastic calculus Introductions to mathematics as needed in order to suit readers at many mathematical levels A companion web site that includes relevant data files as well as all R code and scripts used throughout the book Introduction to Stochastic Processes with R is an ideal textbook for an introductory course in stochastic processes. The book is aimed at undergraduate and beginning graduate-level students in the science, technology, engineering, and mathematics disciplines. The book is also an excellent reference for applied mathematicians and statisticians who are interested in a review of the topic. |
| understanding probability henk tijms: Introduction to Probability and Stochastic Processes with Applications Liliana Blanco Castañeda, Viswanathan Arunachalam, Selvamuthu Dharmaraja, 2014-08-21 An easily accessible, real-world approach to probability and stochastic processes Introduction to Probability and Stochastic Processes with Applications presents a clear, easy-to-understand treatment of probability and stochastic processes, providing readers with a solid foundation they can build upon throughout their careers. With an emphasis on applications in engineering, applied sciences, business and finance, statistics, mathematics, and operations research, the book features numerous real-world examples that illustrate how random phenomena occur in nature and how to use probabilistic techniques to accurately model these phenomena. The authors discuss a broad range of topics, from the basic concepts of probability to advanced topics for further study, including Itô integrals, martingales, and sigma algebras. Additional topical coverage includes: Distributions of discrete and continuous random variables frequently used in applications Random vectors, conditional probability, expectation, and multivariate normal distributions The laws of large numbers, limit theorems, and convergence of sequences of random variables Stochastic processes and related applications, particularly in queueing systems Financial mathematics, including pricing methods such as risk-neutral valuation and the Black-Scholes formula Extensive appendices containing a review of the requisite mathematics and tables of standard distributions for use in applications are provided, and plentiful exercises, problems, and solutions are found throughout. Also, a related website features additional exercises with solutions and supplementary material for classroom use. Introduction to Probability and Stochastic Processes with Applications is an ideal book for probability courses at the upper-undergraduate level. The book is also a valuable reference for researchers and practitioners in the fields of engineering, operations research, and computer science who conduct data analysis to make decisions in their everyday work. |
| understanding probability henk tijms: Chance, Logic and Intuition Steven Tijms, 2021 Chance rules our daily lives in many different ways. From the outcomes of the lottery to the outcomes of medical tests, from the basketball court to the court of law. The ways of chance are capricious. Bizarre things happen all the time. Nevertheless, chance has a logic of its own. It obeys the rules of probability. But if you open a standard book on probability, you may very well feel far removed from everyday life. Abstract formulas and mathematical symbols stare back at you with almost every turn of the page. This book introduces you to the logic of chance without the use of mathematical formulas or symbols. In Part One, you will meet the fascinating pioneers of the mathematics of probability, including Galileo Galilei and Blaise Pascal. Their stories will introduce you, step by step, to the basics of probability. In Part Two, various examples in all areas of daily life will show you how chance defies our expectations time and again. But armed with the basic rules of probability and a good dose of inventiveness, you will be able to unravel the counter-intuitive logic of chance-- |
| understanding probability henk tijms: Introduction to Probability Models Sheldon M. Ross, 2007 Rosss classic bestseller has been used extensively by professionals and as the primary text for a first undergraduate course in applied probability. With the addition of several new sections relating to actuaries, this text is highly recommended by the Society of Actuaries. |
| understanding probability henk tijms: Computational Statistical Physics Lucas Böttcher, Hans J. Herrmann, 2021-08-26 Providing a detailed and pedagogical account of the rapidly-growing field of computational statistical physics, this book covers both the theoretical foundations of equilibrium and non-equilibrium statistical physics, and also modern, computational applications such as percolation, random walks, magnetic systems, machine learning dynamics, and spreading processes on complex networks. A detailed discussion of molecular dynamics simulations is also included, a topic of great importance in biophysics and physical chemistry. The accessible and self-contained approach adopted by the authors makes this book suitable for teaching courses at graduate level, and numerous worked examples and end of chapter problems allow students to test their progress and understanding. |
| understanding probability henk tijms: Quantitative Methods of Data Analysis for the Physical Sciences and Engineering Douglas G. Martinson, 2018-09-20 Provides thorough and comprehensive coverage of new and important quantitative methods in data science, for graduate students and practitioners. |
| understanding probability henk tijms: The Drunkard's Walk Leonard Mlodinow, 2008-05-13 NATIONAL BESTSELLER • From the classroom to the courtroom and from financial markets to supermarkets, an intriguing and illuminating look at how randomness, chance, and probability affect our daily lives that will intrigue, awe, and inspire. “Mlodinow writes in a breezy style, interspersing probabilistic mind-benders with portraits of theorists.... The result is a readable crash course in randomness.” —The New York Times Book Review With the born storyteller's command of narrative and imaginative approach, Leonard Mlodinow vividly demonstrates how our lives are profoundly informed by chance and randomness and how everything from wine ratings and corporate success to school grades and political polls are less reliable than we believe. By showing us the true nature of chance and revealing the psychological illusions that cause us to misjudge the world around us, Mlodinow gives us the tools we need to make more informed decisions. From the classroom to the courtroom and from financial markets to supermarkets, Mlodinow's intriguing and illuminating look at how randomness, chance, and probability affect our daily lives will intrigue, awe, and inspire. |
| understanding probability henk tijms: Markov Decision Processes in Practice Richard J. Boucherie, Nico M. van Dijk, 2017-03-10 This book presents classical Markov Decision Processes (MDP) for real-life applications and optimization. MDP allows users to develop and formally support approximate and simple decision rules, and this book showcases state-of-the-art applications in which MDP was key to the solution approach. The book is divided into six parts. Part 1 is devoted to the state-of-the-art theoretical foundation of MDP, including approximate methods such as policy improvement, successive approximation and infinite state spaces as well as an instructive chapter on Approximate Dynamic Programming. It then continues with five parts of specific and non-exhaustive application areas. Part 2 covers MDP healthcare applications, which includes different screening procedures, appointment scheduling, ambulance scheduling and blood management. Part 3 explores MDP modeling within transportation. This ranges from public to private transportation, from airports and traffic lights to car parking or charging your electric car . Part 4 contains three chapters that illustrates the structure of approximate policies for production or manufacturing structures. In Part 5, communications is highlighted as an important application area for MDP. It includes Gittins indices, down-to-earth call centers and wireless sensor networks. Finally Part 6 is dedicated to financial modeling, offering an instructive review to account for financial portfolios and derivatives under proportional transactional costs. The MDP applications in this book illustrate a variety of both standard and non-standard aspects of MDP modeling and its practical use. This book should appeal to readers for practitioning, academic research and educational purposes, with a background in, among others, operations research, mathematics, computer science, and industrial engineering. |
| understanding probability henk tijms: Lectures on Optimal Transport Luigi Ambrosio, Elia Brué, Daniele Semola, 2024-12-28 This textbook is addressed to PhD or senior undergraduate students in mathematics, with interests in analysis, calculus of variations, probability and optimal transport. It originated from the teaching experience of the first author in the Scuola Normale Superiore, where a course on optimal transport and its applications has been given many times during the last 20 years. The topics and the tools were chosen at a sufficiently general and advanced level so that the student or scholar interested in a more specific theme would gain from the book the necessary background to explore it. After a large and detailed introduction to classical theory, more specific attention is devoted to applications to geometric and functional inequalities and to partial differential equations. This is the second edition of the book, first published in 2018. It includes refinement of proofs, an updated bibliography and a more detailed discussion of minmax principles, with the aim of giving two fully self-contained proofs of Kantorovich duality. |
| understanding probability henk tijms: Introduction to Probability Models, Student Solutions Manual (e-only) Sheldon M. Ross, 2010-01-01 Introduction to Probability Models, Student Solutions Manual (e-only) |
| understanding probability henk tijms: Probability For Dummies Deborah J. Rumsey, 2006-04-03 Packed with practical tips and techniques for solving probability problems Increase your chances of acing that probability exam -- or winning at the casino! Whether you're hitting the books for a probability or statistics course or hitting the tables at a casino, working out probabilities can be problematic. This book helps you even the odds. Using easy-to-understand explanations and examples, it demystifies probability -- and even offers savvy tips to boost your chances of gambling success! Discover how to * Conquer combinations and permutations * Understand probability models from binomial to exponential * Make good decisions using probability * Play the odds in poker, roulette, and other games |
| understanding probability henk tijms: Symmetric Multivariate and Related Distributions Kai Wang Fang, 2018-01-18 Since the publication of the by now classical Johnson and Kotz Continuous Multivariate Distributions (Wiley, 1972) there have been substantial developments in multivariate distribution theory especially in the area of non-normal symmetric multivariate distributions. The book by Fang, Kotz and Ng summarizes these developments in a manner which is accessible to a reader with only limited background (advanced real-analysis calculus, linear algebra and elementary matrix calculus). Many of the results in this field are due to Kai-Tai Fang and his associates and appeared in Chinese publications only. A thorough literature search was conducted and the book represents the latest work - as of 1988 - in this rapidly developing field of multivariate distributions. The authors are experts in statistical distribution theory. |
| understanding probability henk tijms: Maths in Action - Advanced Higher Statistics 1 Ralph Riddiough, John Mccoll, 2000 This is a series of five books each covering a separate unit of the Advanced Higher course. This unit structure gives you the flexibility to put together a complete course or to offer separate units of study. All the books in the series provide: |
| understanding probability henk tijms: Stochastic Modelling and Analysis , 1988 |
| understanding probability henk tijms: Further Mathematics for the Physical Sciences Michael Tinker, Robert Lambourne, 2000-06-08 Further Mathematics for the Physical Sciences Further Mathematics for the Physical Sciences aims to build upon the reader's knowledge of basic mathematical methods, through a gradual progression to more advanced methods and techniques. Carefully structured as a series of self-paced and self-contained chapters, this text covers the essential and most important techniques needed by physical science students. Starting with complex numbers, the text then moves on to cover vector algebra, determinants, matrices, differentiation, integration, differential equations and finally vector calculus, all within an applied environment. The reader is guided through these different techniques with the help of numerous worked examples, applications, problems, figures and summaries. The authors aim to provide high-quality and thoroughly class-tested material to meet the changing needs of science students. Further Mathematics for the Physical Sciences: * Is a carefully structured text, with self-contained chapters. * Gradually introduces mathematical techniques within an applied environment. * Includes many worked examples, applications, problems and summaries in each chapter. Further Mathematics for the Physical Sciences will be invaluable to all students of physics, chemistry and engineering, needing to develop or refresh their knowledge of basic mathematics. The book's structure will make it equally valuable for course use, home study or distance learning. |
| understanding probability henk tijms: Introduction to Probability Theory and Statistical Inference Harold J. Larson, 1974 Discusses probability theory and to many methods used in problems of statistical inference. The Third Edition features material on descriptive statistics. Cramer-Rao bounds for variance of estimators, two-sample inference procedures, bivariate normal probability law, F-Distribution, and the analysis of variance and non-parametric procedures. Contains numerous practical examples and exercises. |
| understanding probability henk tijms: The Joy of Science Richard A. Lockshin, 2007-11-05 Scientists have great passion. What could be more exhilarating than to go to work every day feeling as if you were once again a nine-year-old called up to he stage to help the magician with his trick? To be a researcher is to always be in the position of having the chance to see how the trick works. No wonder that many researchers feel that each new day is the most exciting day to be a scientist. It therefore is not surprising that scientists have such trouble communicating with non-scientists. It is difficult for the scientist to understand a life not focused on the desire to understand. But the differences are not that. Everyone wants to understand; that is one of the factors that make us human. The difference is more that scientists limit their definition of comprehension to specific rules of logic and evidence. These rules apply and are used in everyday life, but often with less rigor or restrictions on evidence. |
| understanding probability henk tijms: The Fundamentals of Political Science Research Paul M. Kellstedt, Guy D. Whitten, 2009 This textbook introduces the scientific study of politics, supplying students with the basic tools to be critical consumers and producers of scholarly research. |
| understanding probability henk tijms: Probability Theory , 2013 Probability theory |
| understanding probability henk tijms: Linear Statistical Models James H. Stapleton, 2009-08-03 Praise for the First Edition This impressive and eminently readable text . . . [is] a welcome addition to the statistical literature. —The Indian Journal of Statistics Revised to reflect the current developments on the topic, Linear Statistical Models, Second Edition provides an up-to-date approach to various statistical model concepts. The book includes clear discussions that illustrate key concepts in an accessible and interesting format while incorporating the most modern software applications. This Second Edition follows an introduction-theorem-proof-examples format that allows for easier comprehension of how to use the methods and recognize the associated assumptions and limits. In addition to discussions on the methods of random vectors, multiple regression techniques, simultaneous confidence intervals, and analysis of frequency data, new topics such as mixed models and curve fitting of models have been added to thoroughly update and modernize the book. Additional topical coverage includes: An introduction to R and S-Plus® with many examples Multiple comparison procedures Estimation of quantiles for regression models An emphasis on vector spaces and the corresponding geometry Extensive graphical displays accompany the book's updated descriptions and examples, which can be simulated using R, S-Plus®, and SAS® code. Problems at the end of each chapter allow readers to test their understanding of the presented concepts, and additional data sets are available via the book's FTP site. Linear Statistical Models, Second Edition is an excellent book for courses on linear models at the upper-undergraduate and graduate levels. It also serves as a comprehensive reference for statisticians, engineers, and scientists who apply multiple regression or analysis of variance in their everyday work. |
| understanding probability henk tijms: Fifty Challenging Problems in Probability with Solutions Frederick Mosteller, 2012-04-26 Remarkable puzzlers, graded in difficulty, illustrate elementary and advanced aspects of probability. These problems were selected for originality, general interest, or because they demonstrate valuable techniques. Also includes detailed solutions. |
| understanding probability henk tijms: Fundamental Probability Marc S. Paolella, 2006-04-05 This publication provides an introduction to the theory and techniques of probability and grew from a set of notes written by the author to accompany a two semester course consisting of senior undergraduate and first year graduate students from quantitative business (50%), economics (40%) and mathematics (10%). |
| understanding probability henk tijms: Introduction to Probability Dimitri Bertsekas, John N. Tsitsiklis, 2008-07-01 An intuitive, yet precise introduction to probability theory, stochastic processes, statistical inference, and probabilistic models used in science, engineering, economics, and related fields. This is the currently used textbook for an introductory probability course at the Massachusetts Institute of Technology, attended by a large number of undergraduate and graduate students, and for a leading online class on the subject. The book covers the fundamentals of probability theory (probabilistic models, discrete and continuous random variables, multiple random variables, and limit theorems), which are typically part of a first course on the subject. It also contains a number of more advanced topics, including transforms, sums of random variables, a fairly detailed introduction to Bernoulli, Poisson, and Markov processes, Bayesian inference, and an introduction to classical statistics. The book strikes a balance between simplicity in exposition and sophistication in analytical reasoning. Some of the more mathematically rigorous analysis is explained intuitively in the main text, and then developed in detail (at the level of advanced calculus) in the numerous solved theoretical problems. |
| understanding probability henk tijms: Signals and Systems Shaila Dinkar Apte, 2016-05-09 Provides rigorous treatment of deterministic and random signals-- |
| understanding probability henk tijms: Probability and Random Processes S. Palaniammal, 2011-06-30 Presents the fundamental concepts and applications of probability and random processes. Beginning with a discussion of probability theory, the text analyses various types of random processes. It also discusses in detail the random variables, standard distributions, correlation and spectral densities, and linear systems. |
| understanding probability henk tijms: Theory of Decision Under Uncertainty Itzhak Gilboa, 2009-03-16 This book describes the classical axiomatic theories of decision under uncertainty, as well as critiques thereof and alternative theories. It focuses on the meaning of probability, discussing some definitions and surveying their scope of applicability. The behavioral definition of subjective probability serves as a way to present the classical theories, culminating in Savage's theorem. The limitations of this result as a definition of probability lead to two directions - first, similar behavioral definitions of more general theories, such as non-additive probabilities and multiple priors, and second, cognitive derivations based on case-based techniques. |
| understanding probability henk tijms: Pluses and Minuses Stefan Buijsman, 2020-08-25 A guide to changing how you think about numbers and mathematics, from the prodigy changing the way the world thinks about math. We all know math is important: we live in the age of big data, our lives are increasingly governed by algorithms, and we're constantly faced with a barrage of statistics about everything from politics to our health. But what might be less obvious is how math factors into your daily life, and what memorizing all of those formulae in school had to do with it. Math prodigy Stefan Buijsman is beginning to change that through his pioneering research into the way we learn math. Plusses and Minuses is based in the countless ways that math is engrained in our daily lives, and shows readers how math can actually be used to make problems easier to solve. Taking readers on a journey around the world to visit societies that have developed without the use of math, and back into history to learn how and why various disciples of mathematics were invented, Buijsman shows the vital importance of math, and how a better understanding of mathematics will give us a better understanding of the world as a whole. Stefan Buijsman has become one of the most sought-after experts in math education after he completed his PhD at age 20. In Plusses and Minuses, he puts his research into practice to help anyone gain a better grasp of mathematics than they have ever had. |
| understanding probability henk tijms: Probability Geoffrey Grimmett, Dominic Welsh, 2014-08-21 Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour. This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields. It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures. The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford. The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem. There is an account of moment generating functions and their applications. The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process. The final chapter is a fairly extensive account of Markov chains in discrete time. This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities. |
| understanding probability henk tijms: The Mathematics of Marriage John M. Gottman, James D. Murray, Catherine C. Swanson, Rebecca Tyson, Kristin R. Swanson, 2005-01-14 Divorce rates are at an all-time high. But without a theoretical understanding of the processes related to marital stability and dissolution, it is difficult to design and evaluate new marriage interventions. The Mathematics of Marriage provides the foundation for a scientific theory of marital relations. The book does not rely on metaphors, but develops and applies a mathematical model using difference equations. The work is the fulfillment of the goal to build a mathematical framework for the general system theory of families first suggested by Ludwig Von Bertalanffy in the 1960s.The book also presents a complete introduction to the mathematics involved in theory building and testing, and details the development of experiments and models. In one marriage experiment, for example, the authors explored the effects of lowering or raising a couple's heart rates. Armed with their mathematical model, they were able to do real experiments to determine which processes were affected by their interventions. Applying ideas such as phase space, null clines, influence functions, inertia, and uninfluenced and influenced stable steady states (attractors), the authors show how other researchers can use the methods to weigh their own data with positive and negative weights. While the focus is on modeling marriage, the techniques can be applied to other types of psychological phenomena as well. |
UNDERSTANDING Definition & Meaning - Merriam-Webster
The meaning of UNDERSTANDING is a mental grasp : comprehension. How to use understanding in a sentence.
UNDERSTANDING | English meaning - Cambridge Dictionary
UNDERSTANDING definition: 1. knowledge about a subject, situation, etc. or about how something works: 2. a particular way in…. Learn more.
Understanding - Wikipedia
Understanding is a cognitive process related to an abstract or physical object, such as a person, situation, or message whereby one is able to use concepts to model that object. …
UNDERSTANDING Definition & Meaning - Dictionary.com
characterized by understanding; prompted by, based on, or demonstrating comprehension, intelligence, discernment, empathy, or the like.
Understanding - Definition, Meaning & Synonyms
The sum of your knowledge of a certain topic, is your understanding of it. This can change, or deepen as you learn more. But being an understanding person doesn't take a lot of studying …
understanding noun - Definition, pictures, pronunciation and …
Definition of understanding noun from the Oxford Advanced Learner's Dictionary. [uncountable, singular] understanding (of something) the knowledge that somebody has about a particular …
UNDERSTANDING definition and meaning | Collins English …
If you have an understanding of something, you know how it works or know what it means. If you are understanding towards someone, you are kind and forgiving. Her boss, who was very …
Understanding - definition of understanding by ... - The Free …
1. the mental process of a person who understands; comprehension; personal interpretation. 2. intellectual faculties; intelligence. 3. knowledge of or familiarity with a particular thing. 5. a …
What does Understanding mean? - Definitions.net
Understanding is a relation between the knower and an object of understanding. Understanding implies abilities and dispositions with respect to an object of knowledge sufficient to support …
514 Synonyms & Antonyms for UNDERSTAND | Thesaurus.com
He described a "mismatch" between the expectation and understanding of the shared owner and the landlord. "It is important that the fate of pesticides and other chemicals in the environment …
UNDERSTANDING Definition & Meaning - Merriam-Webster
The meaning of UNDERSTANDING is a mental grasp : comprehension. How to use understanding in a sentence.
UNDERSTANDING | English meaning - Cambridge Dictionary
UNDERSTANDING definition: 1. knowledge about a subject, situation, etc. or about how something works: 2. a particular way in…. Learn more.
Understanding - Wikipedia
Understanding is a cognitive process related to an abstract or physical object, such as a person, situation, or message whereby one is able to use concepts to model that object. …
UNDERSTANDING Definition & Meaning - Dictionary.com
characterized by understanding; prompted by, based on, or demonstrating comprehension, intelligence, discernment, empathy, or the like.
Understanding - Definition, Meaning & Synonyms
The sum of your knowledge of a certain topic, is your understanding of it. This can change, or deepen as you learn more. But being an understanding person doesn't take a lot of studying …
understanding noun - Definition, pictures, pronunciation and …
Definition of understanding noun from the Oxford Advanced Learner's Dictionary. [uncountable, singular] understanding (of something) the knowledge that somebody has about a particular …
UNDERSTANDING definition and meaning | Collins English …
If you have an understanding of something, you know how it works or know what it means. If you are understanding towards someone, you are kind and forgiving. Her boss, who was very …
Understanding - definition of understanding by ... - The Free …
1. the mental process of a person who understands; comprehension; personal interpretation. 2. intellectual faculties; intelligence. 3. knowledge of or familiarity with a particular thing. 5. a …
What does Understanding mean? - Definitions.net
Understanding is a relation between the knower and an object of understanding. Understanding implies abilities and dispositions with respect to an object of knowledge sufficient to support …
514 Synonyms & Antonyms for UNDERSTAND | Thesaurus.com
He described a "mismatch" between the expectation and understanding of the shared owner and the landlord. "It is important that the fate of pesticides and other chemicals in the environment …
