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Probability for Information Technology
This book introduces probabilistic modelling and explores its role in solving a broad spectrum of engineering problems that arise in Information Technology (IT).Divided into three parts, it begins by laying the foundation of basic probability concepts such as sample space, events, conditional probability, independence, total probability law and random variables.The second part delves into more advanced topics including random processes and key principles like Maximum A Posteriori (MAP) estimation, the law of large numbers and the central limit theorem.The last part applies these principles to various IT domains like communication, social networks, speech recognition, and machine learning, emphasizing the practical aspect of probability through real-world examples, case studies, and Python coding exercises. A notable feature of this book is its narrative style, seamlessly weaving together probability theories with both classical and contemporary IT applications. Each concept is reinforced with tightly-coupled exercise sets, and the associated fundamentals are explored mostly from first principles.Furthermore, it includes programming implementations of illustrative examples and algorithms, complemented by a brief Python tutorial. Departing from traditional organization, the book adopts a lecture-notes format, presenting interconnected themes and storylines.Primarily tailored for sophomore-level undergraduates, it also suits junior and senior-level courses.While readers benefit from mathematical maturity and programming exposure, supplementary materials and exercise problems aid understanding.Part III serves to inspire and provide insights for students and professionals alike, underscoring the pragmatic relevance of probabilistic concepts in IT.
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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 creativity a form of intelligence?
Creativity can be considered a form of intelligence, as it involves the ability to think outside the box, generate original ideas, and solve problems in innovative ways. Creative individuals often demonstrate high levels of cognitive flexibility, which is a key component of intelligence. However, creativity also encompasses emotional and social intelligence, as it involves understanding and expressing oneself in unique and meaningful ways. Therefore, while creativity is a distinct form of intelligence, it also incorporates various aspects of cognitive, emotional, and social intelligence.
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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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What is the probability of the different forms of artificial intelligence?
The probability of different forms of artificial intelligence depends on various factors such as technological advancements, ethical considerations, and societal acceptance. Currently, narrow AI, which is designed for specific tasks, has a high probability of widespread adoption in industries such as healthcare, finance, and transportation. General AI, which possesses human-like cognitive abilities, has a lower probability due to the complexity and ethical concerns surrounding its development. Superintelligent AI, which surpasses human intelligence, has an even lower probability and is the subject of much speculation and debate within the scientific community. Overall, the probability of different forms of artificial intelligence depends on a complex interplay of technological, ethical, and societal factors.
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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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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 : 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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Probability via Expectation
The third edition of 1992 constituted a major reworking of the original text, and the preface to that edition still represents my position on the issues that stimulated me first to write.The present edition contains a number of minor modifications and corrections, but its principal innovation is the addition of material on dynamic programming, optimal allocation, option pricing and large deviations.These are substantial topics, but ones into which one can gain an insight with less labour than is generally thought.They all involve the expectation concept in an essential fashion, even the treatment of option pricing, which seems initially to forswear expectation in favour of an arbitrage criterion.I am grateful to readers and to Springer-Verlag for their continuing interest in the approach taken in this work.Peter Whittle Preface to the Third Edition This book is a complete revision of the earlier work Probability which appeared in 1970.While revised so radically and incorporatingso much new material as to amount to a new text, it preserves both the aim and the approach of the original.That aim was stated as the provision of a 'first text in probability, demanding a reasonable but not extensive knowledge of mathematics, and taking the reader to what one might describe as a good intermediate level' .In doing so it attempted to break away from stereotyped applications, and consider applications of a more novel and significant character.
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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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What are the rules of probability in probability theory?
In probability theory, the rules of probability govern how probabilities are calculated and combined. The rules include the addition rule, which states that the probability of either of two mutually exclusive events occurring is the sum of their individual probabilities. The multiplication rule is used to calculate the probability of two independent events both occurring. Additionally, the complement rule states that the probability of an event not occurring is 1 minus the probability of the event occurring. These rules are fundamental in determining the likelihood of different outcomes in various situations.
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How do you correctly calculate probability in probability theory?
In probability theory, the probability of an event occurring is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. This can be represented as P(A) = (Number of favorable outcomes) / (Total number of possible outcomes). It is important to ensure that all possible outcomes are accounted for and that the favorable outcomes are correctly identified. Additionally, the probability of multiple events occurring can be calculated using the multiplication rule for independent events or the addition rule for mutually exclusive events.
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What is the probability in percent in probability theory?
In probability theory, the probability of an event is a measure of the likelihood that the event will occur. It is usually expressed as a number between 0 and 1, or as a percentage between 0% and 100%. A probability of 0% means the event is impossible, while a probability of 100% means the event is certain to occur. The probability of an event can be calculated using various methods, such as counting outcomes, using probability distributions, or applying statistical techniques.
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With what probability?
With what probability? The probability of an event occurring is a measure of how likely it is to happen, expressed as a number between 0 and 1. The probability of an event that is certain to happen is 1, while the probability of an event that is impossible is 0. Probabilities between 0 and 1 indicate the likelihood of an event occurring, with higher probabilities indicating a greater likelihood.
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