Products related to Probability:
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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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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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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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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 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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Fundamentals of Probability
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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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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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What is the expected value and probability in probability theory?
In probability theory, the expected value is a measure of the central tendency of a random variable. It represents the average value of a random variable over a large number of trials. The expected value is calculated by multiplying each possible outcome by its probability and then summing up these products. Probability, on the other hand, is a measure of the likelihood of a particular event or outcome occurring. It represents the ratio of the number of favorable outcomes to the total number of possible outcomes. Probability theory is used to analyze and predict the likelihood of different outcomes in various situations.
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What is the difference between total probability and conditional probability?
Total probability refers to the probability of an event occurring, taking into account all possible outcomes. It is calculated by summing the probabilities of all possible outcomes. Conditional probability, on the other hand, refers to the probability of an event occurring given that another event has already occurred. It is calculated by dividing the probability of the intersection of the two events by the probability of the given event. In essence, total probability considers all possible outcomes, while conditional probability focuses on the probability of an event given certain conditions.
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