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[null,"1.","Record Nr.",null,"UNINA9910555264603321"]
[null,null,"Autore",null,"Wagaman Amy S. <1982->"]
[null,null,"Titolo",null,"Probability with applications and R / / Amy S. Wagaman, Robert P. Dobrow"]
[null,null,"Pubbl/distr/stampa",null,"Hoboken, New Jersey : , : Wiley, , [2021]"]
[{"$nulls":4},"©2021"]
[null,null,"ISBN",null,"1-5231-4377-0"]
[{"$nulls":4},"1-119-69241-5"]
[{"$nulls":4},"1-119-69243-1"]
[{"$nulls":4},"1-119-69234-2"]
[null,null,"Edizione",null,"[2nd ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource (547 pages)"]
[null,null,"Disciplina",null,"519.502855133"]
[null,null,"Soggetti",null,"Probabilities - Data processing"]
[{"$nulls":4},"Probabilities"]
[{"$nulls":4},"R (Computer program language)"]
[{"$nulls":4},"Electronic books."]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,"Nota di contenuto",null,"Intro -- Contents -- Preface -- Acknowledgments -- About the Companion Website -- Introduction -- Chapter 1 First Principles -- 1.1 Random Experiment, Sample Space, Event -- 1.2 What Is a Probability? -- 1.3 Probability Function -- 1.4 Properties of Probabilities -- 1.5 Equally likely outcomes -- 1.6 Counting I -- 1.6.1 Permutations -- 1.7 Counting II -- 1.7.1 Combinations and Binomial Coefficients -- 1.8 Problem‐Solving Strategies: Complements and Inclusion-Exclusion -- 1.9 A First Look at Simulation -- 1.10 Summary -- Exercises -- Chapter 2 Conditional Probability and Independence -- 2.1 Conditional Probability -- 2.2 New Information Changes the Sample Space -- 2.3 Finding P(A and B) -- 2.3.1 Birthday Problem -- 2.4 Conditioning and the Law of Total Probability -- 2.5 Bayes Formula and Inverting a Conditional Probability -- 2.6 Independence and Dependence -- 2.7 Product Spaces* -- 2.8 Summary -- Exercises -- Chapter 3 INTRODUCTION TO DISCRETE RANDOM VARIABLES -- Learning Outcomes -- 3.1 Random Variables -- 3.2 Independent Random Variables -- 3.3 Bernoulli Sequences -- 3.4 Binomial Distribution -- 3.5 Poisson Distribution -- 3.5.1 Poisson Approximation of Binomial Distribution -- 3.5.2 Poisson as Limit of Binomial Probabilities* -- 3.6 "]
[{"$nulls":4},"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."]
[{"$nulls":4},"Chapter 5 More Discrete Distributions and Their Relationships -- 5.1 Geometric Distribution -- 5.1.1 Memorylessness -- 5.1.2 Coupon Collecting and Tiger Counting -- 5.2 Moment‐Generating Functions -- 5.3 Negative Binomial-Up from the Geometric -- 5.4 Hypergeometric-Sampling Without Replacement -- 5.5 From Binomial to Multinomial -- 5.6 Benford's Law* -- 5.7 Summary -- Exercises -- Chapter 6 Continuous Probability -- 6.1 Probability Density Function -- 6.2 Cumulative Distribution Function -- 6.3 Expectation and Variance -- 6.4 Uniform Distribution -- 6.5 Exponential Distribution -- 6.5.1 Memorylessness -- 6.6 Joint Distributions -- 6.7 Independence -- 6.7.1 Accept-Reject Method -- 6.8 Covariance, Correlation -- 6.9 Summary -- Exercises -- Chapter 7 Continuous Distributions -- 7.1 Normal Distribution -- 7.1.1 Standard Normal Distribution -- 7.1.2 Normal Approximation of Binomial Distribution -- 7.1.3 Quantiles -- 7.1.4 Sums of Independent Normals -- 7.2 Gamma Distribution -- 7.2.1 Probability as a Technique of Integration -- 7.3 Poisson Process -- 7.4 Beta Distribution -- 7.5 Pareto Distribution* -- 7.6 Summary -- Exercises -- Chapter 8 Densities of Functions of Random Variables -- 8.1 Densities via CDFs -- 8.1.1 Simulating a Continuous Random Variable -- 8.1.2 Method of Transformations -- 8.2 Maximums, Minimums, and Order Statistics -- 8.3 Convolution -- 8.4 Geometric Probability -- 8.5 Transformations of Two Random Variables* -- 8.6 Summary -- Exercises -- Chapter 9 Conditional Distribution, Expectation, and Variance -- 9.1 Conditional Distributions -- 9.2 DISCRETE AND CONTINUOUS: MIXING IT UP -- 9.3 CONDITIONAL EXPECTATION -- 9.3.1 From Function to Random Variable -- 9.3.2 Random Sum of Random Variables -- 9.4 COMPUTING PROBABILITIES BY CONDITIONING -- 9.5 CONDITIONAL VARIANCE -- 9.6 BIVARIATE NORMAL DISTRIBUTION* -- 9.7 SUMMARY -- Exercises."]
[{"$nulls":4},"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."]