Probability With Applications and R.

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Detalles Bibliográficos
Autor principal: Dobrow, Robert P.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Newark : John Wiley & Sons, Incorporated, 2013.
Colección:New York Academy of Sciences Ser.
Temas:
Electronic books.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Intro
  • Probability: With Applications and R
  • Copyright
  • Contents
  • Preface
  • Acknowledgments
  • Introduction
  • 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
  • 1.7 Problem-Solving Strategies: Complements, Inclusion-Exclusion
  • 1.8 Random Variables
  • 1.9 A Closer Look at Random Variables
  • 1.10 A First Look at Simulation
  • 1.11 Summary
  • Exercises
  • 2 Conditional Probability
  • 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 Summary
  • Exercises
  • 3 Independence and Independent Trials
  • 3.1 Independence and Dependence
  • 3.2 Independent Random Variables
  • 3.3 Bernoulli Sequences
  • 3.4 Counting II
  • 3.5 Binomial Distribution
  • 3.6 Stirling's Approximation
  • 3.7 Poisson Distribution
  • 3.7.1 Poisson Approximation of Binomial Distribution
  • 3.7.2 Poisson Limit
  • 3.8 Product Spaces
  • 3.9 Summary
  • Exercises
  • 4 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
  • 4.5.1 Indicator Random Variables
  • 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
  • 5 A Bounty of Discrete Distributions
  • 5.1 Geometric Distribution
  • 5.1.1 Memorylessness
  • 5.1.2 Coupon Collecting and Tiger Counting
  • 5.1.3 How R Codes the Geometric Distribution
  • 5.2 Negative Binomial-Up from the Geometric
  • 5.3 Hypergeometric-Sampling Without Replacement
  • 5.4 From Binomial to Multinomial
  • 5.4.1 Multinomial Counts
  • 5.5 Benford's Law
  • 5.6 Summary
  • Exercises
  • 6 Continuous Probability
  • 6.1 Probability Density Function
  • 6.2 Cumulative Distribution Function
  • 6.3 Uniform Distribution
  • 6.4 Expectation and Variance
  • 6.5 Exponential Distribution
  • 6.5.1 Memorylessness
  • 6.6 Functions of Random Variables I
  • 6.6.1 Simulating a Continuous Random Variable
  • 6.7 Joint Distributions
  • 6.8 Independence
  • 6.8.1 Accept-Reject Method
  • 6.9 Covariance, Correlation
  • 6.10 Functions of Random Variables II
  • 6.10.1 Maximums and Minimums
  • 6.10.2 Sums of Random Variables
  • 6.11 Geometric Probability
  • 6.12 Summary
  • Exercises
  • 7 Continuous Distributions
  • 7.1 Normal Distribution
  • 7.1.1 Standard Normal Distribution
  • 7.1.2 Normal Approximation of Binomial Distribution
  • 7.1.3 Sums of Independent Normals
  • 7.2 Gamma Distribution

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