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| probability and statistics for computer science: Probability and Statistics for Computer Science David Forsyth, 2017-12-13 This textbook is aimed at computer science undergraduates late in sophomore or early in junior year, supplying a comprehensive background in qualitative and quantitative data analysis, probability, random variables, and statistical methods, including machine learning. With careful treatment of topics that fill the curricular needs for the course, Probability and Statistics for Computer Science features: • A treatment of random variables and expectations dealing primarily with the discrete case. • A practical treatment of simulation, showing how many interesting probabilities and expectations can be extracted, with particular emphasis on Markov chains. • A clear but crisp account of simple point inference strategies (maximum likelihood; Bayesian inference) in simple contexts. This is extended to cover some confidence intervals, samples and populations for random sampling with replacement, and the simplest hypothesis testing. • A chapter dealing with classification, explaining why it’s useful; how to train SVM classifiers with stochastic gradient descent; and how to use implementations of more advanced methods such as random forests and nearest neighbors. • A chapter dealing with regression, explaining how to set up, use and understand linear regression and nearest neighbors regression in practical problems. • A chapter dealing with principal components analysis, developing intuition carefully, and including numerous practical examples. There is a brief description of multivariate scaling via principal coordinate analysis. • A chapter dealing with clustering via agglomerative methods and k-means, showing how to build vector quantized features for complex signals. Illustrated throughout, each main chapter includes many worked examples and other pedagogical elements such as boxed Procedures, Definitions, Useful Facts, and Remember This (short tips). Problems and Programming Exercises are at the end of each chapter, with a summary of what the reader should know. Instructor resources include a full set of model solutions for all problems, and an Instructor's Manual with accompanying presentation slides. |
| probability and statistics for computer science: Probability and Statistics for Computer Science James L. Johnson, 2011-09-09 Comprehensive and thorough development of both probability and statistics for serious computer scientists; goal-oriented: to present the mathematical analysis underlying probability results Special emphases on simulation and discrete decision theory Mathematically-rich, but self-contained text, at a gentle pace Review of calculus and linear algebra in an appendix Mathematical interludes (in each chapter) which examine mathematical techniques in the context of probabilistic or statistical importance Numerous section exercises, summaries, historical notes, and Further Readings for reinforcement of content |
| probability and statistics for computer science: Probability and Statistics for Computer Scientists Michael Baron, 2013-08-05 Student-Friendly Coverage of Probability, Statistical Methods, Simulation, and Modeling ToolsIncorporating feedback from instructors and researchers who used the previous edition, Probability and Statistics for Computer Scientists, Second Edition helps students understand general methods of stochastic modeling, simulation, and data analysis; make o |
| probability and statistics for computer science: Probability and Statistics with Reliability, Queuing, and Computer Science Applications Kishor S. Trivedi, 2016-07-11 An accessible introduction to probability, stochastic processes, and statistics for computer science and engineering applications Second edition now also available in Paperback. This updated and revised edition of the popular classic first edition relates fundamental concepts in probability and statistics to the computer sciences and engineering. The author uses Markov chains and other statistical tools to illustrate processes in reliability of computer systems and networks, fault tolerance, and performance. This edition features an entirely new section on stochastic Petri nets—as well as new sections on system availability modeling, wireless system modeling, numerical solution techniques for Markov chains, and software reliability modeling, among other subjects. Extensive revisions take new developments in solution techniques and applications into account and bring this work totally up to date. It includes more than 200 worked examples and self-study exercises for each section. Probability and Statistics with Reliability, Queuing and Computer Science Applications, Second Edition offers a comprehensive introduction to probability, stochastic processes, and statistics for students of computer science, electrical and computer engineering, and applied mathematics. Its wealth of practical examples and up-to-date information makes it an excellent resource for practitioners as well. An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department. |
| probability and statistics for computer science: A Modern Introduction to Probability and Statistics F.M. Dekking, C. Kraaikamp, H.P. Lopuhaä, L.E. Meester, 2006-03-30 Many current texts in the area are just cookbooks and, as a result, students do not know why they perform the methods they are taught, or why the methods work. The strength of this book is that it readdresses these shortcomings; by using examples, often from real life and using real data, the authors show how the fundamentals of probabilistic and statistical theories arise intuitively. A Modern Introduction to Probability and Statistics has numerous quick exercises to give direct feedback to students. In addition there are over 350 exercises, half of which have answers, of which half have full solutions. A website gives access to the data files used in the text, and, for instructors, the remaining solutions. The only pre-requisite is a first course in calculus; the text covers standard statistics and probability material, and develops beyond traditional parametric models to the Poisson process, and on to modern methods such as the bootstrap. |
| probability and statistics for computer science: Probability Models for Computer Science Sheldon M. Ross, 2002 The role of probability in computer science has been growing for years and, in lieu of a tailored textbook, many courses have employed a variety of similar, but not entirely applicable, alternatives. To meet the needs of the computer science graduate student (and the advanced undergraduate), best-selling author Sheldon Ross has developed the premier probability text for aspiring computer scientists involved in computer simulation and modeling. The math is precise and easily understood. As with his other texts, Sheldon Ross presents very clear explanations of concepts and covers those probability models that are most in demand by, and applicable to, computer science and related majors and practitioners. Many interesting examples and exercises have been chosen to illuminate the techniques presented Examples relating to bin packing, sorting algorithms, the find algorithm, random graphs, self-organising list problems, the maximum weighted independent set problem, hashing, probabilistic verification, max SAT problem, queuing networks, distributed workload models, and many othersMany interesting examples and exercises have been chosen to illuminate the techniques presented |
| probability and statistics for computer science: All of Statistics Larry Wasserman, 2004-09-17 This book is for people who want to learn probability and statistics quickly. It brings together many of the main ideas in modern statistics in one place. The book is suitable for students and researchers in statistics, computer science, data mining and machine learning. This book covers a much wider range of topics than a typical introductory text on mathematical statistics. It includes modern topics like nonparametric curve estimation, bootstrapping and classification, topics that are usually relegated to follow-up courses. The reader is assumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. The text can be used at the advanced undergraduate and graduate level. Larry Wasserman is Professor of Statistics at Carnegie Mellon University. He is also a member of the Center for Automated Learning and Discovery in the School of Computer Science. His research areas include nonparametric inference, asymptotic theory, causality, and applications to astrophysics, bioinformatics, and genetics. He is the 1999 winner of the Committee of Presidents of Statistical Societies Presidents' Award and the 2002 winner of the Centre de recherches mathematiques de Montreal–Statistical Society of Canada Prize in Statistics. He is Associate Editor of The Journal of the American Statistical Association and The Annals of Statistics. He is a fellow of the American Statistical Association and of the Institute of Mathematical Statistics. |
| probability and statistics for computer science: Probability and Statistics for Data Science Norman Matloff, 2019-06-21 Probability and Statistics for Data Science: Math + R + Data covers math stat—distributions, expected value, estimation etc.—but takes the phrase Data Science in the title quite seriously: * Real datasets are used extensively. * All data analysis is supported by R coding. * Includes many Data Science applications, such as PCA, mixture distributions, random graph models, Hidden Markov models, linear and logistic regression, and neural networks. * Leads the student to think critically about the how and why of statistics, and to see the big picture. * Not theorem/proof-oriented, but concepts and models are stated in a mathematically precise manner. Prerequisites are calculus, some matrix algebra, and some experience in programming. Norman Matloff is a professor of computer science at the University of California, Davis, and was formerly a statistics professor there. He is on the editorial boards of the Journal of Statistical Software and The R Journal. His book Statistical Regression and Classification: From Linear Models to Machine Learning was the recipient of the Ziegel Award for the best book reviewed in Technometrics in 2017. He is a recipient of his university's Distinguished Teaching Award. |
| probability and statistics for computer science: Applied Machine Learning David Forsyth, 2019-07-12 Machine learning methods are now an important tool for scientists, researchers, engineers and students in a wide range of areas. This book is written for people who want to adopt and use the main tools of machine learning, but aren’t necessarily going to want to be machine learning researchers. Intended for students in final year undergraduate or first year graduate computer science programs in machine learning, this textbook is a machine learning toolkit. Applied Machine Learning covers many topics for people who want to use machine learning processes to get things done, with a strong emphasis on using existing tools and packages, rather than writing one’s own code. A companion to the author's Probability and Statistics for Computer Science, this book picks up where the earlier book left off (but also supplies a summary of probability that the reader can use). Emphasizing the usefulness ofstandard machinery from applied statistics, this textbook gives an overview of the major applied areas in learning, including coverage of:• classification using standard machinery (naive bayes; nearest neighbor; SVM)• clustering and vector quantization (largely as in PSCS)• PCA (largely as in PSCS)• variants of PCA (NIPALS; latent semantic analysis; canonical correlation analysis)• linear regression (largely as in PSCS)• generalized linear models including logistic regression• model selection with Lasso, elasticnet• robustness and m-estimators• Markov chains and HMM’s (largely as in PSCS)• EM in fairly gory detail; long experience teaching this suggests one detailed example is required, which students hate; but once they’ve been through that, the next one is easy• simple graphical models (in the variational inference section)• classification with neural networks, with a particular emphasis onimage classification• autoencoding with neural networks• structure learning |
| probability and statistics for computer science: Probabilistic and Statistical Methods in Computer Science Jean-François Mari, René Schott, 2013-04-17 Probabilistic and Statistical Methods in Computer Science presents a large variety of applications of probability theory and statistics in computer science and more precisely in algorithm analysis, speech recognition and robotics. It is written on a self-contained basis: all probabilistic and statistical tools needed are introduced on a comprehensible level. In addition all examples are worked out completely. Most of the material is scattered throughout available literature. However, this is the first volume that brings together all of this material in such an accessible format. Probabilistic and Statistical Methods in Computer Science is intended for students in computer science and applied mathematics, for engineers and for all researchers interested in applications of probability theory and statistics. It is suitable for self study as well as being appropriate for a course or seminar. |
| probability and statistics for computer science: Applied Probability and Statistics Mario Lefebvre, 2007-04-03 This book is based mainly on the lecture notes that I have been using since 1993 for a course on applied probability for engineers that I teach at the Ecole Polytechnique de Montreal. This course is given to electrical, computer and physics engineering students, and is normally taken during the second or third year of their curriculum. Therefore, we assume that the reader has acquired a basic knowledge of differential and integral calculus. The main objective of this textbook is to provide a reference that covers the topics that every student in pure or applied sciences, such as physics, computer science, engineering, etc., should learn in probability theory, in addition to the basic notions of stochastic processes and statistics. It is not easy to find a single work on all these topics that is both succinct and also accessible to non-mathematicians. Because the students, who for the most part have never taken a course on prob ability theory, must do a lot of exercises in order to master the material presented, I included a very large number of problems in the book, some of which are solved in detail. Most of the exercises proposed after each chapter are problems written es pecially for examinations over the years. They are not, in general, routine problems, like the ones found in numerous textbooks. |
| probability and statistics for computer science: Introduction to Probability and Statistics for Science, Engineering, and Finance Walter A. Rosenkrantz, 2008-07-10 Integrating interesting and widely used concepts of financial engineering into traditional statistics courses, Introduction to Probability and Statistics for Science, Engineering, and Finance illustrates the role and scope of statistics and probability in various fields. The text first introduces the basics needed to understand and create |
| probability and statistics for computer science: 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. |
| probability and statistics for computer science: The Probability Companion for Engineering and Computer Science Adam Prügel-Bennett, 2020-01-23 This friendly guide is the companion you need to convert pure mathematics into understanding and facility with a host of probabilistic tools. The book provides a high-level view of probability and its most powerful applications. It begins with the basic rules of probability and quickly progresses to some of the most sophisticated modern techniques in use, including Kalman filters, Monte Carlo techniques, machine learning methods, Bayesian inference and stochastic processes. It draws on thirty years of experience in applying probabilistic methods to problems in computational science and engineering, and numerous practical examples illustrate where these techniques are used in the real world. Topics of discussion range from carbon dating to Wasserstein GANs, one of the most recent developments in Deep Learning. The underlying mathematics is presented in full, but clarity takes priority over complete rigour, making this text a starting reference source for researchers and a readable overview for students. |
| probability and statistics for computer science: Introduction to Probability and Statistics for Engineers and Scientists Sheldon M. Ross, 1987 Elements of probability; Random variables and expectation; Special; random variables; Sampling; Parameter estimation; Hypothesis testing; Regression; Analysis of variance; Goodness of fit and nonparametric testing; Life testing; Quality control; Simulation. |
| probability and statistics for computer science: Think Stats Allen B. Downey, 2011-07-01 If you know how to program, you have the skills to turn data into knowledge using the tools of probability and statistics. This concise introduction shows you how to perform statistical analysis computationally, rather than mathematically, with programs written in Python. You'll work with a case study throughout the book to help you learn the entire data analysis process—from collecting data and generating statistics to identifying patterns and testing hypotheses. Along the way, you'll become familiar with distributions, the rules of probability, visualization, and many other tools and concepts. Develop your understanding of probability and statistics by writing and testing code Run experiments to test statistical behavior, such as generating samples from several distributions Use simulations to understand concepts that are hard to grasp mathematically Learn topics not usually covered in an introductory course, such as Bayesian estimation Import data from almost any source using Python, rather than be limited to data that has been cleaned and formatted for statistics tools Use statistical inference to answer questions about real-world data |
| probability and statistics for computer science: Probability and Statistics Michael J. Evans, Jeffrey S. Rosenthal, 2004 Unlike traditional introductory math/stat textbooks, Probability and Statistics: The Science of Uncertainty brings a modern flavor based on incorporating the computer to the course and an integrated approach to inference. From the start the book integrates simulations into its theoretical coverage, and emphasizes the use of computer-powered computation throughout.* Math and science majors with just one year of calculus can use this text and experience a refreshing blend of applications and theory that goes beyond merely mastering the technicalities. They'll get a thorough grounding in probability theory, and go beyond that to the theory of statistical inference and its applications. An integrated approach to inference is presented that includes the frequency approach as well as Bayesian methodology. Bayesian inference is developed as a logical extension of likelihood methods. A separate chapter is devoted to the important topic of model checking and this is applied in the context of the standard applied statistical techniques. Examples of data analyses using real-world data are presented throughout the text. A final chapter introduces a number of the most important stochastic process models using elementary methods. *Note: An appendix in the book contains Minitab code for more involved computations. The code can be used by students as templates for their own calculations. If a software package like Minitab is used with the course then no programming is required by the students. |
| probability and statistics for computer science: Linear Algebra and Probability for Computer Science Applications Ernest Davis, 2012-05-02 Based on the author's course at NYU, Linear Algebra and Probability for Computer Science Applications gives an introduction to two mathematical fields that are fundamental in many areas of computer science. The course and the text are addressed to students with a very weak mathematical background. Most of the chapters discuss relevant MATLAB functi |
| probability and statistics for computer science: Introduction to Probability Charles Miller Grinstead, James Laurie Snell, 2012-10-30 This text is designed for an introductory probability course at the university level for sophomores, juniors, and seniors in mathematics, physical and social sciences, engineering, and computer science. It presents a thorough treatment of ideas and techniques necessary for a firm understanding of the subject. |
| probability and statistics for computer science: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 The fundamental mathematical tools needed to understand machine learning include linear algebra, analytic geometry, matrix decompositions, vector calculus, optimization, probability and statistics. These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site. |
| probability and statistics for computer science: Probability and Statistics for Engineers Douglas C. Montgomery, 1994-10-03 |
| probability and statistics for computer science: Probability and Computing Michael Mitzenmacher, Eli Upfal, 2005-01-31 Randomization and probabilistic techniques play an important role in modern computer science, with applications ranging from combinatorial optimization and machine learning to communication networks and secure protocols. This 2005 textbook is designed to accompany a one- or two-semester course for advanced undergraduates or beginning graduate students in computer science and applied mathematics. It gives an excellent introduction to the probabilistic techniques and paradigms used in the development of probabilistic algorithms and analyses. It assumes only an elementary background in discrete mathematics and gives a rigorous yet accessible treatment of the material, with numerous examples and applications. The first half of the book covers core material, including random sampling, expectations, Markov's inequality, Chevyshev's inequality, Chernoff bounds, the probabilistic method and Markov chains. The second half covers more advanced topics such as continuous probability, applications of limited independence, entropy, Markov chain Monte Carlo methods and balanced allocations. With its comprehensive selection of topics, along with many examples and exercises, this book is an indispensable teaching tool. |
| probability and statistics for computer science: Mathematics for Computer Science Eric Lehman, F. Thomson Leighton, Albert R. Meyer, 2017-06-05 This book covers elementary discrete mathematics for computer science and engineering. It emphasizes mathematical definitions and proofs as well as applicable methods. Topics include formal logic notation, proof methods; induction, well-ordering; sets, relations; elementary graph theory; integer congruences; asymptotic notation and growth of functions; permutations and combinations, counting principles; discrete probability. Further selected topics may also be covered, such as recursive definition and structural induction; state machines and invariants; recurrences; generating functions. The color images and text in this book have been converted to grayscale. |
| probability and statistics for computer science: Probability and Statistics in the Physical Sciences Byron P. Roe, 2020-09-26 This book, now in its third edition, offers a practical guide to the use of probability and statistics in experimental physics that is of value for both advanced undergraduates and graduate students. Focusing on applications and theorems and techniques actually used in experimental research, it includes worked problems with solutions, as well as homework exercises to aid understanding. Suitable for readers with no prior knowledge of statistical techniques, the book comprehensively discusses the topic and features a number of interesting and amusing applications that are often neglected. Providing an introduction to neural net techniques that encompasses deep learning, adversarial neural networks, and boosted decision trees, this new edition includes updated chapters with, for example, additions relating to generating and characteristic functions, Bayes’ theorem, the Feldman-Cousins method, Lagrange multipliers for constraints, estimation of likelihood ratios, and unfolding problems. |
| probability and statistics for computer science: Introduction to Probability and Statistics for Engineers Milan Holický, 2013-08-04 The theory of probability and mathematical statistics is becoming an indispensable discipline in many branches of science and engineering. This is caused by increasing significance of various uncertainties affecting performance of complex technological systems. Fundamental concepts and procedures used in analysis of these systems are often based on the theory of probability and mathematical statistics. The book sets out fundamental principles of the probability theory, supplemented by theoretical models of random variables, evaluation of experimental data, sampling theory, distribution updating and tests of statistical hypotheses. Basic concepts of Bayesian approach to probability and two-dimensional random variables, are also covered. Examples of reliability analysis and risk assessment of technological systems are used throughout the book to illustrate basic theoretical concepts and their applications. The primary audience for the book includes undergraduate and graduate students of science and engineering, scientific workers and engineers and specialists in the field of reliability analysis and risk assessment. Except basic knowledge of undergraduate mathematics no special prerequisite is required. |
| probability and statistics for computer science: Probability & Statistics Athanasios Papoulis, 1990 A developed, complete treatment of undergraduate probability and statistics by a very well known author. The approach develops a unified theory presented with clarity and economy. Included many examples and applications. Appropriate for an introductory undergraduate course in probability and statistics for students in engineering, math, the physical sciences, and computer science.(vs. Walpole/Myers, Miller/Freund, Devore, Scheaffer/McClave, Milton/Arnold) |
| probability and statistics for computer science: Probability and Statistics Arak M. Mathai, Hans J. Haubold, 2017-12-18 This book offers an introduction to concepts of probability theory, probability distributions relevant in the applied sciences, as well as basics of sampling distributions, estimation and hypothesis testing. As a companion for classes for engineers and scientists, the book also covers applied topics such as model building and experiment design. Contents Random phenomena Probability Random variables Expected values Commonly used discrete distributions Commonly used density functions Joint distributions Some multivariate distributions Collection of random variables Sampling distributions Estimation Interval estimation Tests of statistical hypotheses Model building and regression Design of experiments and analysis of variance Questions and answers |
| probability and statistics for computer science: Python for Probability, Statistics, and Machine Learning José Unpingco, 2019-06-29 This book, fully updated for Python version 3.6+, covers the key ideas that link probability, statistics, and machine learning illustrated using Python modules in these areas. All the figures and numerical results are reproducible using the Python codes provided. The author develops key intuitions in machine learning by working meaningful examples using multiple analytical methods and Python codes, thereby connecting theoretical concepts to concrete implementations. Detailed proofs for certain important results are also provided. Modern Python modules like Pandas, Sympy, Scikit-learn, Tensorflow, and Keras are applied to simulate and visualize important machine learning concepts like the bias/variance trade-off, cross-validation, and regularization. Many abstract mathematical ideas, such as convergence in probability theory, are developed and illustrated with numerical examples. This updated edition now includes the Fisher Exact Test and the Mann-Whitney-Wilcoxon Test. A new section on survival analysis has been included as well as substantial development of Generalized Linear Models. The new deep learning section for image processing includes an in-depth discussion of gradient descent methods that underpin all deep learning algorithms. As with the prior edition, there are new and updated *Programming Tips* that the illustrate effective Python modules and methods for scientific programming and machine learning. There are 445 run-able code blocks with corresponding outputs that have been tested for accuracy. Over 158 graphical visualizations (almost all generated using Python) illustrate the concepts that are developed both in code and in mathematics. We also discuss and use key Python modules such as Numpy, Scikit-learn, Sympy, Scipy, Lifelines, CvxPy, Theano, Matplotlib, Pandas, Tensorflow, Statsmodels, and Keras. This book is suitable for anyone with an undergraduate-level exposure to probability, statistics, or machine learning and with rudimentary knowledge of Python programming. |
| probability and statistics for computer science: Statistics for Data Scientists Maurits Kaptein, Edwin van den Heuvel, 2022-02-27 This book provides an undergraduate introduction to analysing data for data science, computer science, and quantitative social science students. It uniquely combines a hands-on approach to data analysis – supported by numerous real data examples and reusable [R] code – with a rigorous treatment of probability and statistical principles. Where contemporary undergraduate textbooks in probability theory or statistics often miss applications and an introductory treatment of modern methods (bootstrapping, Bayes, etc.), and where applied data analysis books often miss a rigorous theoretical treatment, this book provides an accessible but thorough introduction into data analysis, using statistical methods combining the two viewpoints. The book further focuses on methods for dealing with large data-sets and streaming-data and hence provides a single-course introduction of statistical methods for data science. |
| probability and statistics for computer science: Introductory Statistics 2e Barbara Illowsky, Susan Dean, 2023-12-13 Introductory Statistics 2e provides an engaging, practical, and thorough overview of the core concepts and skills taught in most one-semester statistics courses. The text focuses on diverse applications from a variety of fields and societal contexts, including business, healthcare, sciences, sociology, political science, computing, and several others. The material supports students with conceptual narratives, detailed step-by-step examples, and a wealth of illustrations, as well as collaborative exercises, technology integration problems, and statistics labs. The text assumes some knowledge of intermediate algebra, and includes thousands of problems and exercises that offer instructors and students ample opportunity to explore and reinforce useful statistical skills. This is an adaptation of Introductory Statistics 2e by OpenStax. You can access the textbook as pdf for free at openstax.org. Minor editorial changes were made to ensure a better ebook reading experience. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution 4.0 International License. |
| probability and statistics for computer science: From Algorithms to Z-Scores Norm Matloff, 2009-09 |
| probability and statistics for computer science: Probability and Statistics Applications for Environmental Science Stacey J Shaefer, Louis Theodore, 2007-02-22 Simple, clear, and to the point, Probability and Statistics Applications for Environmental Science delineates the fundamentals of statistics, imparting a basic understanding of the theory and mechanics of the calculations. User-friendliness, uncomplicated explanations, and coverage of example applications in the environmental field set this book ap |
| probability and statistics for computer science: Introduction to Probability with Statistical Applications Géza Schay, 2016-06-17 Now in its second edition, this textbook serves as an introduction to probability and statistics for non-mathematics majors who do not need the exhaustive detail and mathematical depth provided in more comprehensive treatments of the subject. The presentation covers the mathematical laws of random phenomena, including discrete and continuous random variables, expectation and variance, and common probability distributions such as the binomial, Poisson, and normal distributions. More classical examples such as Montmort's problem, the ballot problem, and Bertrand’s paradox are now included, along with applications such as the Maxwell-Boltzmann and Bose-Einstein distributions in physics. Key features in new edition: * 35 new exercises * Expanded section on the algebra of sets * Expanded chapters on probabilities to include more classical examples * New section on regression * Online instructors' manual containing solutions to all exercises“/p> Advanced undergraduate and graduate students in computer science, engineering, and other natural and social sciences with only a basic background in calculus will benefit from this introductory text balancing theory with applications. Review of the first edition: This textbook is a classical and well-written introduction to probability theory and statistics. ... the book is written ‘for an audience such as computer science students, whose mathematical background is not very strong and who do not need the detail and mathematical depth of similar books written for mathematics or statistics majors.’ ... Each new concept is clearly explained and is followed by many detailed examples. ... numerous examples of calculations are given and proofs are well-detailed. (Sophie Lemaire, Mathematical Reviews, Issue 2008 m) |
| probability and statistics for computer science: Probability: A Graduate Course Allan Gut, 2006-03-16 I know it's trivial, but I have forgotten why. This is a slightly exaggerated characterization of the unfortunate attitude of many mathematicians toward the surrounding world. The point of departure of this book is the opposite. This textbook on the theory of probability is aimed at graduate students, with the ideology that rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to chapters on inequalities, characteristic functions, convergence, followed by the three main subjects, the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The main feature of this book is the combination of rigor and detail. Instead of being sketchy and leaving lots of technicalities to be filled in by the reader or as easy exercises, a more solid foundation is obtained by providing more of those not so trivial matters and by integrating some of those not so simple exercises and problems into the body of text. Some results have been given more than one proof in order to illustrate the pros and cons of different approaches. On occasion we invite the reader to minor extensions, for which the proofs reduce to minor modifications of existing ones, with the aim of creating an atmosphere of a dialogue with the reader (instead of the more typical monologue), in order to put the reader in the position to approach any other text for which a solid probabilistic foundation is necessary. Allan Gut is a professor of Mathematical Statistics at Uppsala University, Uppsala, Sweden. He is the author of the Springer monograph Stopped Random Walks (1988), the Springer textbook An Intermediate Course in Probability (1995), and has published around 60 articles in probability theory. His interest in attracting amore general audience to the beautiful world of probability has been manifested in his Swedish popular science book Sant eller Sannolikt (True or Probable), Norstedts förlag (2002). From the reviews: This is more substantial than the usual graduate course in probability; it contains many useful and interesting details that previously were scattered around the literature and gives clear evidence that the writer has a great deal of experience in the area. Short Book Reviews of the International Statistical Institute, December 2005 ...This book is a readable, comprehensive, and up-to-date introductory textbook to probability theory with emphasis on limit theorems for sums and extremes of random variables. The purchase is worth its price. Journal of the American Statistical Association, June 2006 |
| probability and statistics for computer science: Probability and Statistics for Engineering and the Sciences + Enhanced Webassign Access , 2017 |
| probability and statistics for computer science: Introduction to Probability Joseph K. Blitzstein, Jessica Hwang, 2014-07-24 Developed from celebrated Harvard statistics lectures, Introduction to Probability provides essential language and tools for understanding statistics, randomness, and uncertainty. The book explores a wide variety of applications and examples, ranging from coincidences and paradoxes to Google PageRank and Markov chain Monte Carlo (MCMC). Additional application areas explored include genetics, medicine, computer science, and information theory. The print book version includes a code that provides free access to an eBook version. The authors present the material in an accessible style and motivate concepts using real-world examples. Throughout, they use stories to uncover connections between the fundamental distributions in statistics and conditioning to reduce complicated problems to manageable pieces. The book includes many intuitive explanations, diagrams, and practice problems. Each chapter ends with a section showing how to perform relevant simulations and calculations in R, a free statistical software environment. |
| probability and statistics for computer science: A First Course In Probability And Statistics B L S Prakasa Rao, 2008-12-22 Explanation of the basic concepts and methods of statistics requires a reasonably good mathematical background, at least at a first-year-level knowledge of calculus. Most of the statistical software explain how to conduct data analysis, but do not explain when to apply and when not to apply it. Keeping this in view, we try to explain the basic concepts of probability and statistics for students with an understanding of a first course in calculus at the undergraduate level.Designed as a textbook for undergraduate and first-year graduate students in statistics, bio-statistics, social sciences and business administration programs as well as undergraduates in engineering sciences and computer science programs, it provides a clear exposition of the theory of probability along with applications in statistics. The book contains a large number of solved examples and chapter-end exercises designed to reinforce the probability theory and emphasize statistical applications. |
| probability and statistics for computer science: Think Stats Allen B. Downey, 2014-10-16 If you know how to program, you have the skills to turn data into knowledge, using tools of probability and statistics. This concise introduction shows you how to perform statistical analysis computationally, rather than mathematically, with programs written in Python. By working with a single case study throughout this thoroughly revised book, you’ll learn the entire process of exploratory data analysis—from collecting data and generating statistics to identifying patterns and testing hypotheses. You’ll explore distributions, rules of probability, visualization, and many other tools and concepts. New chapters on regression, time series analysis, survival analysis, and analytic methods will enrich your discoveries. Develop an understanding of probability and statistics by writing and testing code Run experiments to test statistical behavior, such as generating samples from several distributions Use simulations to understand concepts that are hard to grasp mathematically Import data from most sources with Python, rather than rely on data that’s cleaned and formatted for statistics tools Use statistical inference to answer questions about real-world data |
| probability and statistics for computer science: Statistics and Probability Theory Michael Havbro Faber, 2012-03-26 This book provides the reader with the basic skills and tools of statistics and probability in the context of engineering modeling and analysis. The emphasis is on the application and the reasoning behind the application of these skills and tools for the purpose of enhancing decision making in engineering. The purpose of the book is to ensure that the reader will acquire the required theoretical basis and technical skills such as to feel comfortable with the theory of basic statistics and probability. Moreover, in this book, as opposed to many standard books on the same subject, the perspective is to focus on the use of the theory for the purpose of engineering model building and decision making. This work is suitable for readers with little or no prior knowledge on the subject of statistics and probability. |
| probability and statistics for computer science: Probability with Applications in Engineering, Science, and Technology Matthew A. Carlton, Jay L. Devore, 2017-03-30 This updated and revised first-course textbook in applied probability provides a contemporary and lively post-calculus introduction to the subject of probability. The exposition reflects a desirable balance between fundamental theory and many applications involving a broad range of real problem scenarios. It is intended to appeal to a wide audience, including mathematics and statistics majors, prospective engineers and scientists, and those business and social science majors interested in the quantitative aspects of their disciplines. The textbook contains enough material for a year-long course, though many instructors will use it for a single term (one semester or one quarter). As such, three course syllabi with expanded course outlines are now available for download on the book’s page on the Springer website. A one-term course would cover material in the core chapters (1-4), supplemented by selections from one or more of the remaining chapters on statistical inference (Ch. 5), Markov chains (Ch. 6), stochastic processes (Ch. 7), and signal processing (Ch. 8—available exclusively online and specifically designed for electrical and computer engineers, making the book suitable for a one-term class on random signals and noise). For a year-long course, core chapters (1-4) are accessible to those who have taken a year of univariate differential and integral calculus; matrix algebra, multivariate calculus, and engineering mathematics are needed for the latter, more advanced chapters. At the heart of the textbook’s pedagogy are 1,100 applied exercises, ranging from straightforward to reasonably challenging, roughly 700 exercises in the first four “core” chapters alone—a self-contained textbook of problems introducing basic theoretical knowledge necessary for solving problems and illustrating how to solve the problems at hand – in R and MATLAB, including code so that students can create simulations. New to this edition • Updated and re-worked Recommended Coverage for instructors, detailing which courses should use the textbook and how to utilize different sections for various objectives and time constraints • Extended and revised instructions and solutions to problem sets • Overhaul of Section 7.7 on continuous-time Markov chains • Supplementary materials include three sample syllabi and updated solutions manuals for both instructors and students |
Probability - Wikipedia
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 …
Probability - Math is Fun
How likely something is to happen. Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability. When a coin is …
Probability - Formula, Calculating, Find, Theorems, Examples
Probability is all about how likely is an event to happen. For a random experiment with sample space S, the probability of happening of an event A is calculated by the probability formula n …
7.5: Basic Concepts of Probability - Mathematics LibreTexts
Define probability including impossible and certain events. Calculate basic theoretical probabilities. Calculate basic empirical probabilities. Distinguish among theoretical, empirical, …
Probability Definition in Math - BYJU'S
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they …
How To Calculate Probability - Math Steps, Examples & Questions
Free how to calculate probability math topic guide, including step-by-step examples, free practice questions, teaching tips and more!
What is Probability? Definition, Types, Formula, & Examples
Apr 7, 2025 · Probability is defined as the measure of how likely an event is to happen, usually expressed as a value between zero and one. A Probability of zero indicates that the event is …
Probability in Maths - GeeksforGeeks
May 16, 2025 · In this section, you will explore the fundamental concepts of probability, key formulas, conditional probability, and Bayes' Theorem. By the end, you'll have a clear …
Probability | Brilliant Math & Science Wiki
A probability is a number that represents the likelihood of an uncertain event. Probabilities are always between 0 and 1, inclusive. The larger the probability, the more likely the event is to …
Probability - Definition, Formula, Types, Terms, Solved Problems
Jan 15, 2021 · Probability is defined as the possibility of an event to occur. The formula for Probability is given as the ratio of the number of favorable events to the total number of …
Probability - Wikipedia
Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 …
Probability - Math is Fun
How likely something is to happen. Many events can't be predicted with total certainty. The best we can say is how likely they are to happen, using the idea of probability. When a coin is …
Probability - Formula, Calculating, Find, Theorems, Examples
Probability is all about how likely is an event to happen. For a random experiment with sample space S, the probability of happening of an event A is calculated by the probability formula n …
7.5: Basic Concepts of Probability - Mathematics LibreTexts
Define probability including impossible and certain events. Calculate basic theoretical probabilities. Calculate basic empirical probabilities. Distinguish among theoretical, empirical, …
Probability Definition in Math - BYJU'S
Probability is a measure of the likelihood of an event to occur. Many events cannot be predicted with total certainty. We can predict only the chance of an event to occur i.e., how likely they are …
How To Calculate Probability - Math Steps, Examples & Questions
Free how to calculate probability math topic guide, including step-by-step examples, free practice questions, teaching tips and more!
What is Probability? Definition, Types, Formula, & Examples
Apr 7, 2025 · Probability is defined as the measure of how likely an event is to happen, usually expressed as a value between zero and one. A Probability of zero indicates that the event is …
Probability in Maths - GeeksforGeeks
May 16, 2025 · In this section, you will explore the fundamental concepts of probability, key formulas, conditional probability, and Bayes' Theorem. By the end, you'll have a clear …
Probability | Brilliant Math & Science Wiki
A probability is a number that represents the likelihood of an uncertain event. Probabilities are always between 0 and 1, inclusive. The larger the probability, the more likely the event is to …
Probability - Definition, Formula, Types, Terms, Solved Problems
Jan 15, 2021 · Probability is defined as the possibility of an event to occur. The formula for Probability is given as the ratio of the number of favorable events to the total number of …
