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Record Nr. |
UNINA9910830192703321 |
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Autore |
Wagaman Amy S. <1982-> |
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Titolo |
Probability with applications and R / / Amy S. Wagaman, Robert P. Dobrow |
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Pubbl/distr/stampa |
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Hoboken, New Jersey : , : Wiley, , [2021] |
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©2021 |
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ISBN |
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1-5231-4377-0 |
1-119-69241-5 |
1-119-69243-1 |
1-119-69234-2 |
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Edizione |
[2nd ed.] |
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Descrizione fisica |
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1 online resource (547 pages) |
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Disciplina |
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Soggetti |
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Probabilities - Data processing |
Probabilities |
R (Computer program language) |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Nota di contenuto |
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Intro -- Contents -- Preface -- Acknowledgments -- About the Companion Website -- Introduction -- Chapter 1 First Principles -- 1.1 Random Experiment, Sample Space, Event -- 1.2 What Is a Probability? -- 1.3 Probability Function -- 1.4 Properties of Probabilities -- 1.5 Equally likely outcomes -- 1.6 Counting I -- 1.6.1 Permutations -- 1.7 Counting II -- 1.7.1 Combinations and Binomial Coefficients -- 1.8 Problem‐Solving Strategies: Complements and Inclusion-Exclusion -- 1.9 A First Look at Simulation -- 1.10 Summary -- Exercises -- Chapter 2 Conditional Probability and Independence -- 2.1 Conditional Probability -- 2.2 New Information Changes the Sample Space -- 2.3 Finding P(A and B) -- 2.3.1 Birthday Problem -- 2.4 Conditioning and the Law of Total Probability -- 2.5 Bayes Formula and Inverting a Conditional Probability -- 2.6 Independence and Dependence -- 2.7 Product Spaces* -- 2.8 Summary -- Exercises -- Chapter 3 INTRODUCTION TO DISCRETE RANDOM VARIABLES -- Learning Outcomes -- 3.1 Random Variables -- 3.2 Independent Random Variables -- 3.3 Bernoulli Sequences -- 3.4 Binomial Distribution -- |
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3.5 Poisson Distribution -- 3.5.1 Poisson Approximation of Binomial Distribution -- 3.5.2 Poisson as Limit of Binomial Probabilities* -- 3.6 Summary -- Exercises -- Chapter 4 Expectation and More with Discrete Random Variables -- 4.1 Expectation -- 4.2 Functions of Random Variables -- 4.3 Joint distributions -- 4.4 Independent Random Variables -- 4.4.1 Sums of Independent Random Variables -- 4.5 Linearity of expectation -- 4.6 Variance and Standard Deviation -- 4.7 Covariance and Correlation -- 4.8 Conditional Distribution -- 4.8.1 Introduction to Conditional Expectation -- 4.9 Properties of Covariance and Correlation* -- 4.10 Expectation of a Function of a Random Variable* -- 4.11 Summary -- Exercises. |
Chapter 5 More Discrete Distributions and Their Relationships -- 5.1 Geometric Distribution -- 5.1.1 Memorylessness -- 5.1.2 Coupon Collecting and Tiger Counting -- 5.2 Moment‐Generating Functions -- 5.3 Negative Binomial-Up from the Geometric -- 5.4 Hypergeometric-Sampling Without Replacement -- 5.5 From Binomial to Multinomial -- 5.6 Benford's Law* -- 5.7 Summary -- Exercises -- Chapter 6 Continuous Probability -- 6.1 Probability Density Function -- 6.2 Cumulative Distribution Function -- 6.3 Expectation and Variance -- 6.4 Uniform Distribution -- 6.5 Exponential Distribution -- 6.5.1 Memorylessness -- 6.6 Joint Distributions -- 6.7 Independence -- 6.7.1 Accept-Reject Method -- 6.8 Covariance, Correlation -- 6.9 Summary -- Exercises -- Chapter 7 Continuous Distributions -- 7.1 Normal Distribution -- 7.1.1 Standard Normal Distribution -- 7.1.2 Normal Approximation of Binomial Distribution -- 7.1.3 Quantiles -- 7.1.4 Sums of Independent Normals -- 7.2 Gamma Distribution -- 7.2.1 Probability as a Technique of Integration -- 7.3 Poisson Process -- 7.4 Beta Distribution -- 7.5 Pareto Distribution* -- 7.6 Summary -- Exercises -- Chapter 8 Densities of Functions of Random Variables -- 8.1 Densities via CDFs -- 8.1.1 Simulating a Continuous Random Variable -- 8.1.2 Method of Transformations -- 8.2 Maximums, Minimums, and Order Statistics -- 8.3 Convolution -- 8.4 Geometric Probability -- 8.5 Transformations of Two Random Variables* -- 8.6 Summary -- Exercises -- Chapter 9 Conditional Distribution, Expectation, and Variance -- 9.1 Conditional Distributions -- 9.2 DISCRETE AND CONTINUOUS: MIXING IT UP -- 9.3 CONDITIONAL EXPECTATION -- 9.3.1 From Function to Random Variable -- 9.3.2 Random Sum of Random Variables -- 9.4 COMPUTING PROBABILITIES BY CONDITIONING -- 9.5 CONDITIONAL VARIANCE -- 9.6 BIVARIATE NORMAL DISTRIBUTION* -- 9.7 SUMMARY -- Exercises. |
Chapter 10 Limits -- 10.1 WEAK LAW OF LARGE NUMBERS -- 10.1.1 Markov and Chebyshev Inequalities -- 10.2 STRONG LAW OF LARGE NUMBERS -- 10.3 METHOD OF MOMENTS* -- 10.4 MONTE CARLO INTEGRATION -- 10.5 CENTRAL LIMIT THEOREM -- 10.5.1 Central Limit Theorem and Monte Carlo -- 10.6 A PROOF OF THE CENTRAL LIMIT THEOREM -- 10.7 SUMMARY -- Exercises -- Chapter 11 Beyond Random Walks And Markov Chains -- 11.1 RANDOM WALKS ON GRAPHS -- 11.1.1 Long‐Term Behavior -- 11.2 RANDOM WALKS ON WEIGHTED GRAPHS AND MARKOV CHAINS -- 11.2.1 Stationary Distribution -- 11.3 FROM MARKOV CHAIN TO MARKOV CHAIN MONTE CARLO -- 11.4 SUMMARY -- Exercises -- Chapter A Probability Distributions in R -- Chapter B Summary of Probability Distributions -- Chapter C Mathematical Reminders -- Chapter D Working with Joint Distributions -- SOLUTIONS TO EXERCISES -- References -- Index -- EULA. |
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Sommario/riassunto |
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"This book is ideal for courses on Probability typically taught in Mathematics and/or Statistics departments but could also be used in Engineering or Data Science departments. This book could also serve as |
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a supplemental or review text for courses on Stochastic Processes or Markov Chains or Brownian Motion, since those require a strong foundation in probability. The text is also preparatory for the Probability Actuarial Exam -- students who successfully complete a course with this text and do well are well-positioned to pass the P exam. Some major features of the new edition include an addition of supplemental materials for coding and simulation, improved exposition and examples for some topics, and addressing issues with errata. These features increase the value of the text especially in an era where developing computing skills has become a staple of statistical practice, and desirable for many other fields as well"-- |
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