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BL
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| Record Number
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860363
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| Main Entry
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Lawrence, Andy,1954-
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| Title & Author
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Probability in physics : : an introductory guide /\ Andy Lawrence.
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| Publication Statement
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Cham :: Springer,, [2019]
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, ©2019
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| Series Statement
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Undergraduate lecture notes in physics,
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| Page. NO
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1 online resource :: illustrations (some color)
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| ISBN
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3030045439
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: 3030045447
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: 9783030045432
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: 9783030045449
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3030045420
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9783030045425
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| Bibliographies/Indexes
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Includes bibliographical references and index.
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| Contents
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Intro; Preface; Aims of the Book; An Overview of the Book; Exercises; Acknowledgements; Contents; Part I The Basics; 1 Randomness and Probability; 1.1 Outline of Content; 1.2 Where Does Unpredictability Come From?; 1.2.1 Incomplete Knowledge; 1.2.2 Large Numbers; 1.2.3 Sensitivity to Initial Conditions; 1.2.4 Open Systems; 1.2.5 Quantum Mechanics; 1.3 Randomness and Probability; 1.4 Probability as Frequency; 1.4.1 Frequencies; 1.4.2 Using the Frequencies as Probabilities; 1.4.3 Continuous Random Variables: Frequency Densities; 1.4.4 The Importance of Relative and Integrated Probabilities
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1.5 Combining Probabilities1.5.1 Probability of A A A A and B B B B; 1.5.2 Combining Continuous Variables; 1.5.3 Bayes's Theorem; 1.5.4 Probability of A A A A or B B B B; 1.5.5 Notation; 1.6 Probability as Degree of Belief; 1.6.1 What Is the ``Correct'' Definition of Probability?; 1.7 Look Ahead; 1.8 Key Concepts; 1.9 Further Reading; 1.10 Exercises; References; 2 Distributions, Moments, and Errors; 2.1 Outline of Content; 2.2 Sample Versus Population Distributions; 2.2.1 Sampling a Discrete Population Distribution; 2.2.2 Sampling a Continuous Population Distribution: Binning
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2.3 Multi-variate Distributions2.3.1 Conditional Distributions; 2.3.2 Marginal Distributions; 2.3.3 Dependence; 2.4 Summarising Quantities for Distributions; 2.4.1 Measures of Location; 2.4.2 Measures of Dispersion; 2.4.3 Percentiles of a Distribution; 2.4.4 Summarising Quantities for Multivariate Distributions; 2.5 Expectation Values and Moments; 2.5.1 Expectation Values; 2.5.2 The Algebra of Expectations; 2.5.3 Moments of a Distribution; 2.5.4 Sample Moments; 2.5.5 Higher Moments: Skewness and Kurtosis; 2.6 Transformation of Probability Distributions
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2.6.1 Transformation of Variance: Univariate Case2.6.2 Transformation of Variance: Bivariate Case; 2.7 Error Analysis; 2.7.1 Types of Error; 2.7.2 Evaluating Errors; 2.8 Key Concepts; 2.9 Further Reading; 2.10 Exercises; References; Part II Frequency Distributions in the Physical World; 3 Counting the Ways: Arrangements and Subsets; 3.1 Outline of Content; 3.2 Balls, Slots, Boxes, and Labels; 3.3 Multi-step Operations; 3.4 Arrangements or Permutations; 3.4.1 Arranging r r r r Things Out of n n n n; 3.5 Subsets or Combinations; 3.6 Partitioning: Macrostates and Microstates
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3.6.1 Two-Box Problems3.6.2 Example: The Two-State Particle Problem; 3.6.3 A First Look at the Second Law of Thermodynamics; 3.6.4 Most Probable Macrostate; 3.7 Multi-box Partitioning; 3.7.1 Maximising Multiplicity for a Multi-box System; 3.7.2 Continuous Systems; 3.8 Systems with Extra Constraints; 3.8.1 Particle Energy Distributions; 3.8.2 Lagrange Multiplier Method; 3.9 Key Concepts; 3.10 Further Reading; 3.11 Exercises; References; 4 Counting Statistics: Binomial and Poisson Distributions; 4.1 Outline of Content; 4.2 The Binomial Distribution; 4.2.1 The Simplest Hit-and-Miss Problem
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| Abstract
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This textbook presents an introduction to the use of probability in physics, treating introductory ideas of both statistical physics and of statistical inference, as well the importance of probability in information theory, quantum mechanics, and stochastic processes, in a unified manner. The book also presents a harmonised view of frequentist and Bayesian approaches to inference, emphasising their complementary value. The aim is to steer a middle course between the "cookbook" style and an overly dry mathematical statistics style. The treatment is driven by real physics examples throughout, but developed with a level of mathematical clarity and rigour appropriate to mid-career physics undergraduates. Exercises and solutions are included.
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| Subject
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Mathematical physics.
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| Subject
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Probabilities.
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| Subject
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Mathematical physics.
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| Subject
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Probabilities.
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| Dewey Classification
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519.2
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| LC Classification
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QC174.85.P76L39 2019eb
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