Products related to Probability:
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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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Probability Models
The purpose of this book is to provide a sound introduction to the study of real-world phenomena that possess random variation.It describes how to set up and analyse models of real-life phenomena that involve elements of chance.Motivation comes from everyday experiences of probability, such as that of a dice or cards, the idea of fairness in games of chance, and the random ways in which, say, birthdays are shared or particular events arise. Applications include branching processes, random walks, Markov chains, queues, renewal theory, and Brownian motion.This textbook contains many worked examples and several chapters have been updated and expanded for the second edition.Some mathematical knowledge is assumed. The reader should have the ability to work with unions, intersections and complements of sets; a good facility with calculus, including integration, sequences and series; and appreciation of the logical development of an argument.Probability Modelsis designed to aid students studying probability as part of an undergraduate course on mathematics or mathematics and statistics.
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Inductive Probability
First published in 1961, Inductive Probability is a dialectical analysis of probability as it occurs in inductions.The book elucidates on the various forms of inductive, the criteria for their validity, and the consequent probabilities.This survey is complemented with a critical evaluation of various arguments concerning induction and a consideration of relation between inductive reasoning and logic.The book promises accessibility to even casual readers of philosophy, but it will hold particular interest for students of Philosophy, Mathematics and Logic.
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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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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 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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Software or hardware?
When deciding between software and hardware, it ultimately depends on the specific needs and goals of the user. Software provides flexibility, scalability, and ease of updates, making it ideal for tasks that require frequent changes or updates. On the other hand, hardware offers reliability, security, and performance for tasks that require high processing power or data storage. It is important to carefully evaluate the requirements of the project or task at hand to determine whether software or hardware is the best solution.
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'Software or hardware?'
The choice between software and hardware depends on the specific needs and goals of the user. Software provides flexibility and can be easily updated or customized, while hardware offers physical components that may be more reliable and provide better performance for certain tasks. Ultimately, the decision between software and hardware should be based on the specific requirements of the user and the intended use of the technology.
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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 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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Introduction to Probability
Unlike most probability textbooks, which are often written only for the mathematically-oriented students, Mark Ward and Ellen Gundlach's Introduction to Probability makes the subject much more accessible, reaching out to a much wider introductory-level audience. Its approachable and conversational style, highly visual approach, practical examples, and step-by-step problem solving procedures help all kinds of students understand the basics of probability theory and its broad applications in the outside world. This textbook has been extensively class-tested throughout its preliminary edition in order to make it even more effective at building confidence in students who have viable problem-solving potential but are not fully comfortable in the realm of mathematics.Its rich pedagogy, combined with a thoughtful structure, provides an accessible introduction to this complex subject.
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Probability and Measure
Praise for the Third Edition "It is, as far as I'm concerned, among the best books in math ever written....if you are a mathematician and want to have the top reference in probability, this is it." (Amazon.com, January 2006) A complete and comprehensive classic in probability and measure theory Probability and Measure, Anniversary Edition by Patrick Billingsley celebrates the achievements and advancements that have made this book a classic in its field for the past 35 years.Now re-issued in a new style and format, but with the reliable content that the third edition was revered for, this Anniversary Edition builds on its strong foundation of measure theory and probability with Billingsley's unique writing style.In recognition of 35 years of publication, impacting tens of thousands of readers, this Anniversary Edition has been completely redesigned in a new, open and user-friendly way in order to appeal to university-level students. This book adds a new foreward by Steve Lally of the Statistics Department at The University of Chicago in order to underscore the many years of successful publication and world-wide popularity and emphasize the educational value of this book.The Anniversary Edition contains features including: An improved treatment of Brownian motionReplacement of queuing theory with ergodic theoryTheory and applications used to illustrate real-life situationsOver 300 problems with corresponding, intensive notes and solutionsUpdated bibliographyAn extensive supplement of additional notes on the problems and chapter commentaries Patrick Billingsley was a first-class, world-renowned authority in probability and measure theory at a leading U.S. institution of higher education. He continued to be an influential probability theorist until his unfortunate death in 2011.Billingsley earned his Bachelor's Degree in Engineering from the U.S.Naval Academy where he served as an officer. he went on to receive his Master's Degree and doctorate in Mathematics from Princeton University.Among his many professional awards was the Mathematical Association of America's Lester R.Ford Award for mathematical exposition. His achievements through his long and esteemed career have solidified Patrick Billingsley's place as a leading authority in the field and been a large reason for his books being regarded as classics. This Anniversary Edition of Probability and Measure offers advanced students, scientists, and engineers an integrated introduction to measure theory and probability.Like the previous editions, this Anniversary Edition is a key resource for students of mathematics, statistics, economics, and a wide variety of disciplines that require a solid understanding of probability theory.
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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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