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Python for Probability, Statistics, and Machine Learning
Using a novel integration of mathematics and Python codes, this book illustrates the fundamental concepts that link probability, statistics, and machine learning, so that the reader can not only employ statistical and machine learning models using modern Python modules, but also understand their relative strengths and weaknesses.To clearly connect theoretical concepts to practical implementations, the author provides many worked-out examples along with "Programming Tips" that encourage the reader to write quality Python code.The entire text, including all the figures and numerical results, is reproducible using the Python codes provided, thus enabling readers to follow along by experimenting with the same code on their own computers. Modern Python modules like Pandas, Sympy, Scikit-learn, Statsmodels, Scipy, Xarray, Tensorflow, and Keras are used to implement and visualize important machine learning concepts like the bias/variance trade-off, cross-validation, interpretability, and regularization.Many abstract mathematical ideas, such as modes of convergence in probability, are explained and illustrated with concrete numerical examples. This book is suitable for anyone with undergraduate-level experience with probability, statistics, or machine learning and with rudimentary knowledge of Python programming.
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Teaching Probability
Written by leading subject specialists, Teaching Probability is designed to support teaching concepts in probability by providing a new approach to this difficult subject from a perspective not limited by a syllabus, giving teachers both theoretical and practical knowledge of an innovative way of teaching probability.This alternative approach to teaching probability focuses on the methods that teachers can apply to help their students engage with the topic using experiments and mathematical models to solve problems, considering how to overcome common misconceptions and the way in which probability can be communicated.
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Probability Essentials
We have made small changes throughout the book, including the exercises, and we have tried to correct if not all, then at least most of the typos.We wish to thank the many colleagues and students who have commented c- structively on the book since its publication two years ago, and in particular Professors Valentin Petrov, Esko Valkeila, Volker Priebe, and Frank Knight.Jean Jacod, Paris Philip Protter, Ithaca March, 2002 Preface to the Second Printing of the Second Edition We have bene?ted greatly from the long list of typos and small suggestions sent to us by Professor Luis Tenorio.These corrections have improved the book in subtle yet important ways, and the authors are most grateful to him.Jean Jacod, Paris Philip Protter, Ithaca January, 2004 Preface to the First Edition We present here a one semester course on Probability Theory.We also treat measure theory and Lebesgue integration, concentrating on those aspects which are especially germane to the study of Probability Theory.The book is intended to ?ll a current need: there are mathematically sophisticated s- dents and researchers (especially in Engineering, Economics, and Statistics) who need a proper grounding in Probability in order to pursue their primary interests.Many Probability texts available today are celebrations of Pr- ability Theory, containing treatments of fascinating topics to be sure, but nevertheless they make it di?cult to construct a lean one semester course that covers (what we believe) are the essential topics.
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Fundamentals of Probability
Praise for the fourth edition:"This book is an excellent primer on probability ….The flow of the text aids its readability, and the book is indeed a treasure trove of set and solved problems. --Dalia Chakrabarty, Brunel University, UK"This textbook provides a thorough and rigorous treatment of fundamental probability, including both discrete and continuous cases.The book’s ample collection of exercises gives instructors and students a great deal of practice and tools to sharpen their understanding." --Joshua Stangle, University of Wisconsin – Superior, USAThis one- or two-term calculus-based basic probability text is written for majors in mathematics, physical sciences, engineering, statistics, actuarial science, business and finance, operations research, and computer science.It presents probability in a natural way: through interesting and instructive examples and exercises that motivate the theory, definitions, theorems, and methodology.This book is mathematically rigorous and, at the same time, closely matches the historical development of probability.Whenever appropriate, historical remarks are included, and the 2096 examples and exercises have been carefully designed to arouse curiosity and hence encourage students to delve into the theory with enthusiasm. New to the Fifth Edition:In this edition, a significant change has been made in the order of material presentation. The topics such as the joint probability mass function, joint probability density functions, independence of random variables, sums of random variables, the central limit theorem, and certain other materials have been covered earlier in the book, enabling students to grasp these crucial concepts from the start.These changes have considerable merit, particularly the idea of covering the celebrated central limit theorem immediately after discussing the normal distribution.Additionally, discussions on sigma fields are provided and an in-depth section on characteristic functions is added.The central limit theorem has been proven using both moment-generating functions and characteristic functions. In the present edition, numerous new figures are included that were drawn for the first time, specifically to aid in students’ understanding of the material.These fresh illustrations, along with all the previous ones in the book, have been meticulously crafted by the technical support team at CRC. Instructors who prefer the content arrangement used in previous editions can still teach the material in the same order as those editions.Moreover, the homepage of this book contains a whole chapter with comprehensive coverage on Stochastic Processes as well as additional contents for Chapters 1 to 10, such as extra examples, supplementary topics, and practical applications to facilitate in-depth exploration.Furthermore, it offers thorough solutions for all self-tests and self-quiz problems, empowering students to assess their progress and grasp of this demanding subject. In this new edition, at the end of select chapters, sections are included dedicated to exploring approximate solutions for complex probabilistic problems using simulation techniques.These simulations are conducted using the R software, a powerful tool well-suited for probabilistic simulations due to its extensive collection of built-in functions and numerous specialized libraries designed for various simulation purposes.In the homepage of the book, a chapter, titled “Algorithm-Driven Simulations,” is presented in which we delve deeply into the concept of simulation using algorithms exclusively, without being tied to any specific programming language.
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Is learning programming and software development very challenging?
Learning programming and software development can be challenging for some people, as it requires logical thinking, problem-solving skills, and attention to detail. However, with dedication, practice, and the right resources, it is definitely achievable. Breaking down complex concepts into smaller, more manageable parts and seeking help from online tutorials, courses, and communities can make the learning process easier and more enjoyable. Ultimately, the level of challenge will vary depending on the individual's background, experience, and learning style.
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Which programming languages are used in software development?
There are many programming languages used in software development, including popular languages such as Java, Python, C++, JavaScript, and Ruby. Each language has its own strengths and is used for different purposes in software development. For example, Java is commonly used for building enterprise-level applications, while Python is known for its simplicity and versatility. C++ is often used for system software and game development, while JavaScript is essential for web development. Overall, the choice of programming language depends on the specific requirements of the software being developed.
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What is the difference between software development and programming?
Software development is a broader term that encompasses the entire process of creating software, including planning, designing, testing, and maintaining software applications. Programming, on the other hand, refers specifically to the act of writing code to instruct a computer to perform certain tasks. While programming is a key component of software development, software development involves a more comprehensive approach that includes various stages beyond just writing code.
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What training opportunities are available for IT specialists to specialize in web development and general programming, such as software development?
There are various training opportunities available for IT specialists looking to specialize in web development and general programming. Online platforms like Coursera, Udemy, and Codecademy offer courses and certifications in programming languages such as Python, Java, and JavaScript. Additionally, coding bootcamps like General Assembly and Flatiron School provide intensive, hands-on training in software development. IT specialists can also pursue advanced degrees in computer science or related fields to deepen their knowledge and skills in web development and programming.
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High-Probability Trading
"The Goal Is to Teach All Traders to Think with the Mindset of a Successful Trader..." While successful trading requires tremendous skill and knowledge, it begins and ends with mindset.What do exceptional traders think when they purchase a quality stock and the price immediately plummets?How do they keep one bad trade from destroying their confidence - and bankroll?What do they know that the rest of us don't? "Some trades are not worth the risk and should never be done."High Probability Trading" shows you how to trade only when the odds are in your favor.From descriptions of the software and equipment an exceptional trader needs high probability signals that either a top or bottom has been reached, it is today's most complete guidebook to thinking like an exceptional trader - every day, on every trade. "It's not how good you are at one individual thing, but it's the culmination of every aspect of trading that makes one successful."Before he became a successful trader, Marcel Link spent years wading from one system to the next, using trial and error to figure out what worked, what didn't, and why. In "High Probability Trading", Link reveals the steps he took to become a consistent, patient, and winning trader - by learning what to watch for, what to watch out for, and what to do to make each trade a high probability trade. "Why do a select few traders repeatedly make money while the masses lose?What do bad traders do that good traders avoid, and what do winning traders do that is different?Throughout this book I will detail how successful traders behave differently and consistently make money by making high probability trades and avoiding common pitfalls..." - From the preface.Within 6 months of beginning their careers full of promise and hope, most traders are literally out of money and out of trading. "High Probability Trading" reduces the likelihood that you will have to pay this "traders' tuition," by detailing a market-proven program for weathering those first few months and becoming a profitable trader from the beginning.Combining a uniquely blunt look at the realities of trading with examples, charts, and case studies detailing actual hits and misses of both short- and long-term traders, this straightforward guidebook discusses: the 10 consistent attributes of a successful trader, and how to make them work for you; strategies for controlling emotions in the heat of trading battle; technical analysis methods for identifying trends, breakouts, reversals, and more; market-tested signals for consistently improving the timing of entry and exit points; how to "trade the news" - and understand when the market has already discounted it; and learning how to get out of a bad trade before it can hurt you. The best traders enter the markets only when the odds are in their favor. "High Probability Trading" shows you how to know the difference between low and high probability situations, and only trade the latter.It goes far beyond simply pointing out the weaknesses and blind spots that hinder most traders to explaining how those defects can be understood, overcome, and turned to each trader's advantage.While it is a cliche, it is also true that there are no bad traders, only bad trades.Let "High Probability Trading" show you how to weed the bad trades from your trading day by helping you see them before they occur.Packed with charts, trading tips, and questions traders should be asking themselves, plus real examples of traders in every market situation, this powerful book will first give you the knowledge and tools you need to tame the markets and then show you how to meld them seamlessly into a customized trading program - one that will help you join the ranks of elite traders and increase your probability of success on every trade.
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Probability with Martingales
Probability theory is nowadays applied in a huge variety of fields including physics, engineering, biology, economics and the social sciences.This book is a modern, lively and rigorous account which has Doob's theory of martingales in discrete time as its main theme.It proves important results such as Kolmogorov's Strong Law of Large Numbers and the Three-Series Theorem by martingale techniques, and the Central Limit Theorem via the use of characteristic functions.A distinguishing feature is its determination to keep the probability flowing at a nice tempo.It achieves this by being selective rather than encyclopaedic, presenting only what is essential to understand the fundamentals; and it assumes certain key results from measure theory in the main text.These measure-theoretic results are proved in full in appendices, so that the book is completely self-contained.The book is written for students, not for researchers, and has evolved through several years of class testing.Exercises play a vital rôle. Interesting and challenging problems, some with hints, consolidate what has already been learnt, and provide motivation to discover more of the subject than can be covered in a single introduction.
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Probability For Dummies
Learn how to calculate your chances with easy-to-understand explanations of probability Probability—the likelihood or chance of an event occurring—is an important branch of mathematics used in business and economics, finance, engineering, physics, and beyond.We see probability at work every day in areas such as weather forecasting, investing, and sports betting.Packed with real-life examples and mathematical problems with thorough explanations, Probability For Dummies helps students, professionals, and the everyday reader learn the basics.Topics include set theory, counting, permutations and combinations, random variables, conditional probability, joint distributions, conditional expectations, and probability modeling.Pass your probability class and play your cards right, with this accessible Dummies guide.Understand how probability impacts daily lifeDiscover what counting rules are and how to use themPractice probability concepts with sample problems and explanationsGet clear explanations of all the topics in your probability or statistics class Probability For Dummies is the perfect Dummies guide for college students, amateur and professional gamblers, investors, insurance professionals, and anyone preparing for the actuarial exam.
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Probability : An Introduction
Probability is an area of mathematics of tremendous contemporary importance across all aspects of human endeavour.This book is a compact account of the basic features of probability and random processes at the level of first and second year mathematics undergraduates and Masters' students in cognate fields.It is suitable for a first course in probability, plus a follow-up course in random processes including Markov chains. A special feature is the authors' attention to rigorous mathematics: not everything is rigorous, but the need for rigour is explained at difficult junctures.The text is enriched by simple exercises, together with problems (with very brief hints) many of which are taken from final examinations at Cambridge and Oxford.The first eight chapters form a course in basic probability, being an account of events, random variables, and distributions - discrete and continuous random variables are treated separately - together with simple versions of the law of large numbers and the central limit theorem.There is an account of moment generating functions and their applications.The following three chapters are about branching processes, random walks, and continuous-time random processes such as the Poisson process.The final chapter is a fairly extensive account of Markov chains in discrete time. This second edition develops the success of the first edition through an updated presentation, the extensive new chapter on Markov chains, and a number of new sections to ensure comprehensive coverage of the syllabi at major universities.
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What training options are available for IT specialists to specialize in web development and general programming, such as software development?
IT specialists looking to specialize in web development and general programming have a variety of training options available to them. They can pursue formal education through degree programs in computer science or related fields, attend coding bootcamps that offer intensive training in programming languages and frameworks, or take online courses and tutorials to learn specific skills. Additionally, IT specialists can participate in workshops, seminars, and conferences to stay updated on the latest trends and technologies in web development and software development. Continuous learning and practice are essential for IT specialists to excel in these specialized areas.
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What distinguishes conditional probability from independent probability?
Conditional probability is the probability of an event occurring given that another event has already occurred. It takes into account the information about the occurrence of one event when calculating the probability of another event. Independent probability, on the other hand, is the probability of one event occurring without any influence from the occurrence of another event. In other words, conditional probability is influenced by the occurrence of a specific event, while independent probability is not influenced by any other event.
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Which programming language is suitable for software development for the PC?
There are several programming languages that are suitable for software development for the PC, but some of the most popular and widely used ones include C++, Java, and C#. C++ is a powerful and versatile language that is commonly used for developing system software and applications that require high performance. Java is a popular choice for developing cross-platform applications, as it can run on any operating system that has a Java Virtual Machine. C# is commonly used for developing Windows applications and is well-integrated with the .NET framework. Ultimately, the choice of programming language depends on the specific requirements of the software being developed and the preferences of the development team.
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What is a probability space in probability theory?
A probability space in probability theory consists of three components: a sample space, an event space, and a probability measure. The sample space is the set of all possible outcomes of an experiment, the event space is a collection of subsets of the sample space representing different events, and the probability measure assigns a probability to each event in the event space. Together, these components define the mathematical framework for analyzing the likelihood of different outcomes in a probabilistic setting.
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