**Best Reference Books on Probability**, which are used by students of top universities, and colleges. This will help you choose the right book depending on if you are a beginner or an expert. Here is the complete list of

**Probability Books**with their authors, publishers, and an unbiased review of them as well as links to the Amazon website to directly purchase them. If permissible, you can also download the free PDF books on Probability below.

- Introduction to Probability and Random Processes
- Introduction to Probability Theory
- Advanced Probability Theory
- Probability and Statistics
- Probability, Random Process and Statistical Inference
- Probabilistic Models

## 1. Introduction to Probability and Random Processes

1."Conditional Independence in Applied Probability" by P Pfeiffer
Book Review: The book presents a thorough understanding of probability through various theories and applications, including real-life examples from fields such as biology, computer science, cryptology, ecology, public health, and sports. It emphasizes simulation and showcases computational and theoretical results, with chapters on topics such as conditional probability, independent trials, random variables, discrete and continuous distributions, and continuous probability. The book is also replete with problems of probability and practical examples, making it ideal for undergraduate courses on probability.
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2."Probability and computing: Randomized Algorithms and Probabilistic Analysis" by Mitzenmacher and E Upfal
“Probability and computing: Randomized Algorithms and Probabilistic Analysis” Book Review: This book gives a thorough introduction to probability and computing. It discusses randomized algorithms and probabilistic analysis, covering a wide range of applications from machine learning and combinatorial optimization to communication networks and secure protocols. It is designed for beginning graduate and advanced undergraduate students studying computer science and applied mathematics. The book offers an interesting introduction to the techniques and paradigms used in developing probabilistic algorithms and analyses. It includes numerous examples and applications to enhance understanding.
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3."Introduction to Probability" by D Bertsekas and J Tsitsiklis
Book Review: This book offers a comprehensive introduction to probability theory, stochastic processes, and probabilistic models widely applied in various disciplines such as science, engineering, economics, and more. It serves as an ideal textbook for both graduate and undergraduate students studying probability. The book covers fundamental topics including probabilistic models, discrete and continuous random variables, limit theorems, least squares estimation, bivariate normal distribution, as well as important concepts like Bernoulli, Poisson, and Markov processes. It provides a solid foundation in probability theory for readers across different fields.
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4."Probability, Random Variables, and Random Processes" by John J Shynk
“Probability, Random Variables, and Random Processes” Book Review: This comprehensive book on probability theory provides a rigorous mathematical framework for random variables and random processes, and features several appendices covering related material on integration, inequalities and identities, frequency domain transforms, and linear algebra. It covers statistics in detail and their connection to parameter estimation techniques, making it an ideal resource for students and teachers covering topics such as communication systems, information theory, adaptive filtering, optimal filtering, and antenna beamforming.
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5."Probability and Random Processes" by S Palaniammal
“Probability and Random Processes” Book Review: This comprehensive book on probability and random processes offers fundamental concepts and real-world applications in engineering and technology, including Computer Science and Engineering, Electronics and Communication Engineering, Biomedical Engineering, and Information Technology. It begins with an explanation of probability theory, followed by an analysis of various types of random processes. The book also covers random variables, correlation, standard distributions, and spectral densities, and presents the topics in a well-organized sequence with appropriate explanations and simple mathematical formulas.
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6."Theory of Probability and Random Processes" by Leonid B Koralov and Yakov G Sinai
“Theory of Probability and Random Processes” Book Review: This book provides a fundamental and self-contained explanation of classical probability theory and theory of random processes, including Lebesgue integration, random walks, laws of large numbers, Markov chains, limit theorems, and their relation to renormalization group theory. It also covers the theory of stationary random processes, Brownian motion, and generalized random processes, making it an ideal resource for students and teachers seeking a detailed overview of probability and random processes.
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7."Probability Theory, Random Processes and Mathematical Statistics" by Y Rozanov Rozanov
“Probability Theory, Random Processes and Mathematical Statistics” Book Review: This book offers a thorough exploration of probability theory, random processes, and mathematical statistics. It encompasses essential domains of contemporary mathematics and their practical applications. The book facilitates the construction of robust models to effectively handle diverse random phenomena encountered in real-world scenarios. It equips readers with a plethora of tools for analyzing, predicting, and controlling random phenomena. Designed with students and teachers of undergraduate and graduate courses in mind, this book caters to a wide range of academic levels and provides valuable insights for learners in various disciplines.
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8."Probability, Random Processes, and Statistical Analysis" by Hisashi Kobayashi Brian L Mark William Turin
“Probability, Random Processes, and Statistical Analysis” Book Review: This book offers a comprehensive overview of probability, random processes, and statistical analysis, covering a wide range of advanced topics and their practical applications. It provides an extensive treatment of Bayesian vs. frequentist statistics, spectral representation, inequalities, time series, and bound and unbound approximation, as well as maximum likelihood estimation, the expectation maximization algorithm, and geometric Brownian motion. The book also covers specialized applications, such as Markov models, Baum Welch algorithms, machine learning algorithms, queueing theory, Wiener and Kalman filters, and loss networks, in great detail.
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9."Probability and Random Processes for Electrical and Computer Engineers" by John A Gubner
“Probability and Random Processes for Electrical and Computer Engineers” Book Review: This book offers a comprehensive introduction to probability and random processes, emphasizing their significance as valuable tools for engineers in explaining, modeling, analyzing, and designing technology. It assumes a basic understanding of probability and proceeds to explain more complex topics that are required at the graduate level. The initial chapters cover the fundamentals of probability, including discrete and continuous random variables. Later chapters delve into more specialized topics such as Gaussian random vectors, random vectors, random processes, convergence, and Markov Chains. The book provides a solid foundation for readers to comprehend and apply these concepts in practical settings.
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10."Schaum's Outline of Probability, Random Variables, and Random Processes" by Hwei P Hsu
“Schaum’s Outline of Probability, Random Variables, and Random Processes” Book Review: This book aims to present a comprehensive overview of all the important processes and concepts underlying probability. The chapters are structured to be precise and explain each concept in a step-by-step manner. The book covers fundamental topics such as probability, random variables, and random processes, as well as advanced topics like limit theorem, analysis and processing of random processes, estimation theory, decision theory, queuing theory, and information theory. It features over 400 solved problems, examples, and practice exercises to help readers develop their problem-solving skills. Detailed videos featuring instructors explaining key problems are also included. The book delves into specialized topics such as Gaussian random vectors, random vectors, random processes, convergence, and Markov Chains. It is designed to help readers build confidence, develop skills, and gain knowledge to excel academically. Effective problem-solving techniques are introduced and supported by numerous solved and unsolved problems.
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11."Introduction to Measure and Probability" by K R Parthasarathy
“Introduction to Measure and Probability” Book Review: This book is a masterful blend of the aesthetic and practical aspects of measure and probability. Its chapters cover all major topics related to probability, including Boolean algebra, extension of measures, Borel maps, integration, measures on product spaces, Hilbert space, weak convergence of probability measures, and invariant measures on groups. The theorems and proofs are described efficiently, and many exercises and examples are included to aid understanding. The book is ideal for both undergraduate and graduate students seeking knowledge in measure theory and probability theory.
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12."Probability, Reliability and Statistical Methods in Engineering Design" by Haldar A and Mahadevan S
Book Review: This book presents the fundamental principles of reliability and statistics that are necessary for risk-based engineering analysis and provides a clear presentation of design concepts. It includes numerous examples that explain the risk-based design concepts in the field of reliability and statistics. The book covers a range of concepts and skills required for reliability assessments, as well as many reliability assessment methods and concepts necessary for implementing risk-based design in practical problems. Additionally, the book explains both risk-based and deterministic design concepts.
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13."Convergence of Probability Measures" by P Billingsley
“Convergence of Probability Measures” Book Review: This textbook is written in an easy-to-read style, incorporating all the essential topics required for a detailed understanding of the subject with a straightforward approach that is reader-friendly. It has been updated with the classic work “Convergence of Probability Measures” to reflect recent developments in the field. The book provides a clear, precise, and up-to-date account of probability limit theory in metric spaces. With many examples illustrating the power, applications, and utility of this theory in various disciplines such as statistics, engineering, economics, and population biology, the book maintains a smooth transition while keeping the subject matter simple. Topics covered include Weak Convergence in Metric Spaces, The Space C & D, Dependent Variables, Other Modes of Convergence, and appendices, problems, Bibliographical Notes, and Bibliography.
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## 2. Introduction to Probability Theory

1."Probability and Measure" by P Billingsley
“Probability and Measure” Book Review: This book presents a comprehensive introduction to measure theory and probability, including the latest developments in the field. It has been updated with a new style and format, while maintaining reliable content. With a unique writing style, the book covers the foundations of measure theory and probability in an easily understandable language, and includes many real-life examples. Numerous problems with corresponding intensive notes and clear solutions are included, covering topics such as probability, measures, integration, random variables, convergence of distribution, derivatives, conditional probability, stochastic processes, Brownian motion, Kolmogorov’s existence theorem, martingales, and more. The book also deals with stochastic processes and provides appendices and problematic notes for better understanding. A bibliography and list of symbols are provided at the end of the book.
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2."Introduction to Probability" by P G Hoel
“Introduction to probability theory” Book Review: This book covers probability spaces, combinatorial analysis, discrete random variables and their expectations, as well as continuous random variables, jointly distributed random variables and expectations, and the central limit theorem. In addition, it discusses moment generating functions, characteristic functions, random walks, and Poisson processes.
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3."A First Look at Rigorous Probability Theory" by J S Rosenthal
“A First Look at Rigorous Probability Theory” Book Review: This book provides a clear introduction to probability theory using measure theory. It presents the material in a simple manner and offers complete proofs for all essential introductory results. The book focuses on integrating measure theory and mathematical details through intuitive probabilistic concepts, rather than treating them as separate subjects. It includes exercises and additional topics to provide a comprehensive overview. The book is suitable for graduate students in various fields such as mathematics, statistics, economics, management, finance, computer science, and engineering. It covers a wide range of topics including the need for measure theory, probability triples, probabilistic foundations, expected values, convergence and inequalities, distributions of random variables, stochastic processes, discrete Markov chains, probability theorems, weak convergence, characteristic functions, probability law decomposition, conditional probability, martingales, and general stochastic processes. It is designed for graduate and Ph.D. students specializing in engineering, economics, and management.
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4."Probability with Applications" by M Woodroofe
“Probability with Applications” Book Review: This book covers the classical model, axiomatic probability, conditional probability, and independence. It also discusses binomial probabilities, random variables, random vectors, distribution theory, and limit theorems.
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5."An Introduction to Probability Theory and its Applications" by William Feller
“An Introduction to Probability theory and its Applications” Book Review: This book begins by introducing the fundamental nature of probability theory. It covers essential concepts such as sample space, elements of combinatorial analysis, fluctuations in coin tossing, and random walks. Additionally, it discusses the combination of events and combination probability. The book also delves into binomial and Poisson distributions, Markov chains, and time-dependent stochastic processes. Each chapter concludes with a set of problems accompanied by their solutions, enhancing the reader’s understanding and application of the material.
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6."An Introduction To Probability Theory" by Das | |

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7."An Introduction to Probability Theory and Mathematical Statistics" by Vijay K Rohatgi
“An Introduction to Probability Theory and Mathematical Statistics” Book Review: This book is structured into three parts, providing a comprehensive coverage of probability theory and mathematical statistics. It offers a substantial collection of nearly 550 problems accompanied by their solutions, along with 350 worked examples and 200 remarks to further enhance understanding. Specifically designed for upper-undergraduate and graduate-level students specializing in probability and statistics, this book is designed to meet the needs of students pursuing these fields of study.
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8."An Introduction to Statistical Learning: with Applications in R" by Gareth James and Daniela Witten
“An Introduction to Statistical Learning: with Applications in R” Book Review: This book begins by providing a comprehensive introduction to statistical learning. It covers essential topics such as linear regression, classification, resampling methods, linear model selection and regularization, as well as exploring advanced concepts beyond regularity. Additionally, the book delves into tree-based methods, support vector machines, and unsupervised learning. Each chapter concludes with exercises, allowing readers to practice and reinforce their understanding of the material.
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9."An Introduction to Probability Theory and Its Applications Vol 2" by William Feller | |

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10."A Natural Introduction to Probability Theory" by R Meester | |

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11."An Introduction to Probability Theory and its Applications" by W Feller
“An Introduction to Probability Theory and its Applications” Book Review: This book is divided into three parts. The first part provides an overview of probability theory and mathematical statistics, covering topics such as sample spaces, combinatorial analysis, fluctuations in coin tossing and random walks, the combination of events, types of distributions, Markov chains, and stochastic processes. The second part focuses on practical applications of probability theory, including many real-world examples. The final part delves into advanced topics such as martingale theory, Brownian motion, calculus, and statistical inference.
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12."Probability Essentials" by Jean Jacod and Philip E Protter
Book Review: This book is a valuable resource for graduate-level courses in probability theory. It offers significant benefits to students and teachers in the fields of finance theory, electrical engineering, and operations research. In addition to covering essential topics, the book includes a dedicated chapter on martingale theory and explores advanced subjects such as Brownian motion, calculus, and statistical inference. With approximately 28 chapters, the book assumes a prerequisite of basic knowledge in mathematics.
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13."Probability Measures on Metric Spaces" by K R Parthasarathy
“Probability Measures on Metric Spaces” Book Review: This book offers a thorough introduction to the topic, covering separable metric groups, locally compact abelian groups, Hilbert spaces, and the spaces of continuous functions. The seven chapters include topics such as the Borel Subsets of a Metric Space, Probability Measures in a Metric Space, Probability Measures in a Metric Group, Probability Measures in Locally Compact Abelian Groups, the Kolmogorov Consistency Theorem and Conditional Probability, Probability Measures in a Hilbert Space, and Probability Measures on C[0, 1] and D[0, 1]. Each chapter starts with an introduction and progresses through the material, beginning with an overview of the isomorphism theorem and then discussing tightness, regularity, and perfectness of measures defined on metric spaces. This book is designed for statisticians and those interested in the topic.
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14."Theory of Probability" by Parimal Mukhopadhyay
“Theory of Probability” Book Review: This book presents a balanced mixture of the classical and modern axiomatic approaches to the theory of probability. It covers topics such as univariate distributions, bivariate normal distributions, multinomial distribution, and convergence of random variables. The book provides explanatory notes, examples, and exercises, and is suitable for graduate-level students with a basic knowledge of mathematics. Worked-out examples and exercises with hints are also included.
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15."Probability Theory: The Logic of Science" by E T Jaynes and G Larry Bretthorst
“Probability Theory: The Logic of Science” Book Review: This book is structured into two parts, each focusing on different aspects of probability theory. The first part covers principles and elementary applications, while the second part delves into advanced applications. Designed for readers with a solid foundation in applied mathematics at an advanced undergraduate level or beyond, this book explores the applications of probability theory to a diverse range of problems in physics, mathematics, economics, chemistry, and biology. With a strong emphasis on practical learning, the book offers numerous exercises and problems to enhance understanding and proficiency in the subject matter.
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16."Probability concepts in Engineering Planning and Design" by A H S Ang and W H Tang
Book Review: This book discusses the methodologies and concepts used to evaluate uncertainty significance in the area of system performance and design. It covers concepts of probability and statistics that are used for quality control processes and practical concepts and probability applications related to engineering. It is suitable for engineers who require a working knowledge of the basic concepts of probability, and contains numerous problems and solutions.
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17."Applied Statistics and Probability for Engineers" by Douglas C Montgomery and G C Runger
Book Review: This textbook is a practical approach to chemical sciences, physical sciences, and engineering, and is an excellent resource for courses in probability and statistics. The book emphasizes real engineering applications and solutions, and includes material on bootstrap, P value usage, equivalence testing, and p values combination. Numerous examples are provided throughout the book.
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## 3. Advanced Probability Theory

1."A Course in Probability Theory" by K L Chung
“A Course in Probability Theory” Book Review: This book serves as a valuable resource for both instructors and students, offering a comprehensive supplement for the subject matter. The text is highly adaptable, providing instructors with guidance on how to incorporate it into their syllabus. With numerous well-illustrated examples, including special cases, readers will gain a solid understanding of the topic through numerical exercises. The book covers a wide range of topics, including Distribution function, Measure theory, Random variable Expectation Independence, Convergence concepts, Law of large numbers Random series, Characteristic function, Central limit theorem and its ramifications, Random walk, Conditioning Markov property Martingale, Measure and Integral, and more.
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2."Advanced Probability Theory" by Janos Galambos
“Advanced Probability Theory” Book Review: This is a comprehensive and insightful book that delves into the intricacies of probability theory. Divided into several well-structured chapters, the book covers a wide range of topics. These include distribution functions, limit theorems, central limit theorems, laws of large numbers, random walks, branching processes, martingales, Brownian motion, and much more. Galambos’s writing style is clear and concise, making complex concepts accessible to readers. With its thorough coverage and rigorous approach, “Advanced Probability Theory” serves as an invaluable resource for students and researchers alike seeking a deep understanding of probability theory.
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3."Probability Theory: A Concise Course" by Y A Rozanov
“Probability Theory: A Concise Course” Book Review: This book provides an excellent overview of the theory and practice of probability, assuming some prior mathematical knowledge from the reader. It offers a comprehensive treatment of the subject with numerous practical applications. The text is resourceful, fast-moving, and self-contained, starting with basic concepts before moving onto more complex topics such as dependent variables and events. The book covers Probability and Relative Frequency, Rudiments of Combinatorial Analysis, Elementary Events, The Sample Space, The Addition Law for Probabilities, Conditional Probability, Statistical Independence, Discrete and Continuous Random Variables, Distribution Functions, Mathematical Expectation, Chebyshev’s Inequality, The Variance and Correlation Coefficient, Bernoulli Trials, The Binomial and Poisson Distributions, The De Moivre-Laplace Theorem, The Central Limit Theorem, Transition Probabilities, Persistent and Transient States, Limiting Probabilities, Kolmogorov Equations, Stationary Distributions, Definitions, Sojourn Time, More on Limiting Probabilities, and includes appendices along with problems at the end of each topic.
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4."Real Analysis and Probability" by R M Dudley
“Real Analysis and Probability” Book Review: This graduate-level book provides an introduction to both measure and integration theory and functional analysis, with a focus on their interplay with probability measures. The text covers Foundations: set theory, General topology, Measures, Integration, Lp spaces: introduction to functional analysis, Convex sets and duality of normed spaces, Measure, topology, and differentiation, Introduction to probability theory, Measurability, Stochastic processes, Convergence of laws on separable metric spaces, Conditional expectations and martingales, Convergence of laws and central limit theorems, and includes ample numerical exercises with solutions provided chapter-wise.
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5."Probability Theory: An Advanced Course" by Vivek S Borkar
“Probability Theory: An Advanced Course” Book Review: This book takes a selective approach to topics in probability theory, focusing on areas relevant to modern research in stochastic processes. The book assumes a solid foundation in mathematics and begins with a rapid overview of the basics. Each chapter provides detailed coverage of the topic at hand, including Spaces of Probability Measures, Conditioning and Martingales, Basic Limit Theorems, Markov Chains, Foundations of Continuous-Time Processes, Conditioning and Martingales, Conditional Expectations, Strong Law of Large Numbers, Central Limit Theorem, Markov Chains, Stationary Distributions, Transient and Null Recurrent Chains, Separability and Measurability, Skorohod’s Theorem, Monotone Class Theorems, Random Variables, and additional exercises at the end of each chapter.
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6."Random Processes: Filtering, Estimation and Detection" by Lonnie C Ludeman
“Random Processes: Filtering, Estimation and Detection” Book Review: This book explores the key principles and practical applications of random processes, with a particular emphasis on Filtering, Estimation, and Detection. Random processes play a vital role in various fields of engineering, such as information theory, computer vision, digital signal processing, vibration theory, and stress analysis. The ability to identify, measure, and analyze random processes in noisy environments is a crucial task in the study and design of modern communication technologies and signal processing algorithms. The book covers the fundamentals of probability and random processes through filtering, calculation, and identification, with an extensive focus on detection and estimation theory. The main topics covered in the text include probability and characterizations of random variables and random processes, the optimal principle of estimation (Wiener and Kalman filters), and the theory of detection for both isolated and continuous-time measurements. These subjects are closely related and interconnected, providing a comprehensive understanding of random processes and their applications.
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## 4. Probability and Statistics

1."Introduction to Probability and Statistics" by J S Milton and J C Arnold
“Introduction to Probability and Statistics” Book Review: The book presents an introduction to basic probability theory and statistical inference through illustrations. The author has included topics such as practical approaches to methods of statistical modeling and data analysis, in line with the latest syllabus of various universities in India. Each chapter provides a detailed description and a large number of solved numerical examples drawn from various university examinations. Diagrams are used to make the topics more understandable.
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2."Miller and Freund’s Probability and Statistics for Engineers" by R A Johnson and C B Gupta
“Miller and Freund’s Probability and Statistics for Engineers” Book Review: This book is designed for engineering students and teachers, providing an introduction to probability and statistics. It includes computer exercises for MINITAB software and explains graphs of the sampling distribution to show the critical region and p-value. The book covers various concepts, including basic and advanced concepts of Probability, Statistics, and Random Variable, in a balanced presentation of theory and application. Exam patterns and the latest research results are included for wider scope of preparation. Each chapter has descriptions, examples, laws, and important points for revision, as well as summary tables of testing performance, a checklist of key terms, and statistical guidelines.
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3."Probability and Statistics for Engineers and Scientists" by Walpole R E
“Probability and Statistics for Engineers and Scientists” Book Review: This book is for undergraduate chemical and mechanical engineering students, providing simple and concise explanations of concepts in a logical manner. The focus is on applied problems, including an introduction to basic probability theory and statistical inference. Diagrams are clear and error-free, with standard and simple procedures for deriving equations and ample solved examples.
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4."Statistics for Engineers and Scientists" by Navidi W
“Statistics for Engineers and Scientists” Book Review: This textbook takes a practical approach to methods of statistical modeling and data analysis, presenting the subject as both a science and an art. Theories and explanations are supported by a large number of solved examples, with additional figures for clarity. Multiple choice and other pedagogically arranged questions help students assess their knowledge. The book is designed primarily for undergraduate and postgraduate students, as well as undergraduate students of engineering.
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5."An Introduction to Probability and Statistics" by Vijay K Rohatgi and A K Md Ehsanes Saleh
“An Introduction to Probability and Statistics” Book Review: This book provides solutions and exercises for readers to gain maximum knowledge, with chapters on basic concepts of Probability, Statistics, and Random Variable. Other important topics include the theory of error functions, conditional probability, binomial distribution, etc. Solved examples are included in every chapter, making it beneficial for students pursuing BA and B.Com courses (Pass and Honours), postgraduate students of Arts and Commerce, and students preparing for competitive examinations.
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6."Probability and Statistics (Schaum’s Outline Series)" by Murray Spiegel and John Schiller
“Probability and Statistics (Schaum’s Outline Series)” Book Review: This book serves as a guideline for statistics and probability courses across the country, containing solved problems and examples for easy learning. Practicing exercises will sharpen problem-solving skills, and an outline of the course information is provided for testing skills. The book covers various topics, including binomial distribution, normal distribution, conditional probability, and variance analysis. It has been revised from time-to-time to contain all relevant changes happening each year, highlighting important facts to shorten study time and achieve high scores.
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7."Probability and Statistics for Engineers and Scientists" by Walpole
“Probability and Statistics for Engineers and Scientists” Book Review: This book combines analytical rigour with accessibility, with new chapters added to the existing edition, such as histogram, hypothesis, covariance, independent events, mean, and median. The book includes numerous examples and exercise questions for practice and testing of concepts, as well as an introduction to basic concepts of Probability, Statistics, and Random Variable, with excellent references and clearly labeled diagrams. The book is beneficial for students preparing for competitive examinations and undergraduate students.
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8."Probability - Statistics and Random Processes" by Veerarajan
“Probability – Statistics and Random Processes” Book Review: This book targets undergraduate engineering students and provides a clear explanation of basic concepts of Probability, Statistics, and Random Variable, including an introduction to basic probability theory and statistical inference. The book covers other important chapters such as law of large numbers, independent events, normal distribution, and scatter diagram.
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9."Probability and Statistics" by E Rukmangadachari
“Probability and Statistics” Book Review: This textbook aims to help students perceive Probability, Statistics, and Random Variable as both a science and an art. The basic concepts are presented with theories, explanations, and a large number of solved examples. Additional figures are added for clarity and understanding. Pedagogically arranged questions, including multiple-choice questions, are provided to help students assess their knowledge. Designed primarily as a textbook for undergraduate and postgraduate students, this book is also useful for undergraduate engineering students.
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10."Probability and Statistics with Reliability, Queuing and Computer Science Applications" by Trivedi
“Probability and Statistics with Reliability, Queuing and Computer Science Applications” Book Review: The book presents statistics and probability in a clear and concise manner, covering the syllabus of almost all universities. It is suitable for both undergraduate and graduate students, as well as teachers. The end-of-chapter exercises are organized into three categories: descriptive, analytical, and objective, providing readers with a comprehensive tool to test their understanding of the subject. The book systematically introduces practical approaches to methods of statistical modeling and data analysis, treating the methods of analysis and interpretation of probability theory and statistical inference in a logical sequence. The book maintains a unique balance between theory and methodology, presented in a clear and unambiguous manner with well-formulated worked-out examples demonstrating their design applications.
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11."Advances in Combinatorial Methods and Applications to Probability and Statistics" by N Balakrishnan | |

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## 5. Probability, Random Process and Statistical Inference

1."Probabilities, Random Variables and Random Processes" by Peyton Peebles
“Probabilities, Random Variables and Random Processes” Book Review: This updated and revised book covers the latest theories on probability, random variables, and random signal principles. Practical applications of probability concepts are highlighted throughout the text, and the content is reinforced by a large number of exercises. The information presented in the book is easily understandable for readers. It is appropriate for junior-senior level courses in electrical engineering.
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2."Probability, Random Variables and Stochastic Processes" by A Papoulis
“Probability, Random Variables and Stochastic Processes” Book Review: This up-to-date edition of the book covers the fundamental principles and basic applications of probability, random variables, and stochastic processes. The chapters of the book provide a comprehensive coverage of repeated trials, Bernoulli’s theorem, random variables, various probability distributions, parameter estimation in statistics, Poisson processes, Markov chains and processes, and queueing theory. Numerous examples are included in the text to facilitate readers’ comprehension. The book is recommended for senior or graduate level courses in probability and is valuable for students studying mathematics, physics, and electrical engineering.
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3."Probability, Random Processes and Estimation Theory for Engineers" by H Stark and J W Woods | |

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4."Probability and Random Processes" by Geoffrey R Grimmett and David R Stirzaker
“Probability and Random Processes” Book Review: This book presents a thorough and rigorous introduction to the field of probability theory, with a detailed focus on random processes. The aim of the book is to provide an accessible yet comprehensive introduction to probability theory, covering many important topics and providing examples of major random processes. The chapters are self-contained and organized, with a detailed description of each process. The book includes topics such as sampling, Markov chains, Monte Carlo methods, geometric probability, coupling, Poisson approximation, large deviations, spatial Poisson processes, renewal-reward, queueing networks, and stochastic calculus. The text also includes many exercises and problems for self-study and self-assessment. This book is suitable for undergraduate courses in mathematics, statistics, and the sciences.
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5."Probability and Random Processes for Electrical Engineering" by Albert Leon-Garcia
“Probability and Random Processes for Electrical Engineering” Book Review: This book offers a proper introduction to probability and random processes, with comprehensive and precise chapters. It provides suitable processes and methods for transitioning real problems into probability models and helps readers improve their problem-solving skills. The text features many practical applications of probability theory in electrical and computer engineering to provide relatable content. The book also covers discrete-time random processes, illustrating the relationship between random variables and continuous-time random processes. A section of the book is dedicated to random processes.
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## 6. Probabilistic Models

1."Introduction to Probability Models" by Sheldon M Ross
Book Review: This book presents an introduction to probability theory and stochastic processes, including heuristic and non-rigorous concepts of probability using measure theory tools. It covers the basics of probability such as random variables, conditional probability, and conditional expectation. Additionally, the book discusses stochastic processes, Poisson processes, and Markov chains, as well as queuing, reliability theory, and simulation. It is a valuable resource for students studying probability in engineering, computer science, management, and operations research.
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2."Introduction to Probability Models: Operations Research" by Wayne L Winston
Book Review: This book explores various probability models from financial engineering, computational simulation, and manufacturing engineering, emphasizing practical breakthroughs and making ideas accessible. With a balance of theoretical concepts and examples, the book also includes numerous problems and exercises covering a wide range of probability topics.
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3."Introduction to Probability" by Dimitri P Bertsekas and John N Tsitsiklis
Book Review: This comprehensive probability textbook covers introduction to probability theory, stochastic processes, and probabilistic models used in science, engineering, economics, and related fields. It is suitable for both graduate and undergraduate students, covering fundamentals of probability theory as well as advanced topics such as transforms, sums of random variables, least square estimation, bivariate normal distribution, Bernoulli, Poisson, and Markov processes. Numerous solved theoretical problems are also included.
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3."Reasoning with Probabilistic and Deterministic Graphical Models: Exact Algorithms" by Dechter
“Reasoning with Probabilistic and Deterministic Graphical Models: Exact Algorithms” Book Review: This book provides an introduction to graphical models, including exact algorithms for reasoning with such models and all important principles. It covers topics such as inference-based and message-passing schemes, search-based conditioning schemes, bucket elimination for probabilistic networks, tree-clustering schemes, algorithms for graphical models, and more. It will be beneficial for researchers and students in artificial intelligence and machine learning, and beyond.
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4."Probabilistic Graphical Models" by Van Der Gaag
“Probabilistic Graphical Models” Book Review: This comprehensive book explores the various aspects of graphical models in probabilistic reasoning, decision making, and learning. With thirty-eight revised full papers, it provides in-depth insights into these topics. The content of the book draws inspiration from the 7th International Workshop on Probabilistic Graphical Models, which took place in the Netherlands in September 2014.
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5."Probabilistic Models for Nonlinear Partial Differential Equations" by Carl Graham
“Probabilistic Models for Nonlinear Partial Differential Equations” Book review: This book provides a detailed discussion on weak convergence of stochastic integrals, the probabilistic interpretation, particle approximation of equations, and modeling of networks by interacting particle systems. The text also uses basic laws and principles of physics such as conservation laws, Boltzmann-like and Navier-Stokes equations. It is a valuable resource for PhD students, young researchers, and probabilists working on stochastic particle methods and the approximation of SPDEs.
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