Introduction to Probability and Statistics Using R
Free

Introduction to Probability and Statistics Using R

By G. Jay Kerns
Free
Book Description

This is a textbook for an undergraduate course in probability and statistics. The approximate prerequisites are two or three... More > semesters of calculus and some linear algebra. Students attending the class include mathematics, engineering, and computer science majors.

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Table of Contents
  • Contents
  • Preface
  • List of Figures
  • List of Tables
  • 1 An Introduction to Probability and Statistics
    • 1.1 Probability
    • 1.2 Statistics
    • Chapter Exercises
  • 2 An Introduction to R
    • 2.1 Downloading and Installing R
    • 2.2 Communicating with R
    • 2.3 Basic R Operations and Concepts
    • 2.4 Getting Help
    • 2.5 External Resources
    • 2.6 Other Tips
    • Chapter Exercises
  • 3 Data Description
    • 3.1 Types of Data
    • 3.2 Features of Data Distributions
    • 3.3 Descriptive Statistics
    • 3.4 Exploratory Data Analysis
    • 3.5 Multivariate Data and Data Frames
    • 3.6 Comparing Populations
    • Chapter Exercises
  • 4 Probability
    • 4.1 Sample Spaces
    • 4.2 Events
    • 4.3 Model Assignment
    • 4.4 Properties of Probability
    • 4.5 Counting Methods
    • 4.6 Conditional Probability
    • 4.7 Independent Events
    • 4.8 Bayes' Rule
    • 4.9 Random Variables
    • Chapter Exercises
  • 5 Discrete Distributions
    • 5.1 Discrete Random Variables
    • 5.2 The Discrete Uniform Distribution
    • 5.3 The Binomial Distribution
    • 5.4 Expectation and Moment Generating Functions
    • 5.5 The Empirical Distribution
    • 5.6 Other Discrete Distributions
    • 5.7 Functions of Discrete Random Variables
    • Chapter Exercises
  • 6 Continuous Distributions
    • 6.1 Continuous Random Variables
    • 6.2 The Continuous Uniform Distribution
    • 6.3 The Normal Distribution
    • 6.4 Functions of Continuous Random Variables
    • 6.5 Other Continuous Distributions
    • Chapter Exercises
  • 7 Multivariate Distributions
    • 7.1 Joint and Marginal Probability Distributions
    • 7.2 Joint and Marginal Expectation
    • 7.3 Conditional Distributions
    • 7.4 Independent Random Variables
    • 7.5 Exchangeable Random Variables
    • 7.6 The Bivariate Normal Distribution
    • 7.7 Bivariate Transformations of Random Variables
    • 7.8 Remarks for the Multivariate Case
    • 7.9 The Multinomial Distribution
    • Chapter Exercises
  • 8 Sampling Distributions
    • 8.1 Simple Random Samples
    • 8.2 Sampling from a Normal Distribution
    • 8.3 The Central Limit Theorem
    • 8.4 Sampling Distributions of Two-Sample Statistics
    • 8.5 Simulated Sampling Distributions
    • Chapter Exercises
  • 9 Estimation
    • 9.1 Point Estimation
    • 9.2 Confidence Intervals for Means
    • 9.3 Confidence Intervals for Differences of Means
    • 9.4 Confidence Intervals for Proportions
    • 9.5 Confidence Intervals for Variances
    • 9.6 Fitting Distributions
    • 9.7 Sample Size and Margin of Error
    • 9.8 Other Topics
    • Chapter Exercises
  • 10 Hypothesis Testing
    • 10.1 Introduction
    • 10.2 Tests for Proportions
    • 10.3 One Sample Tests for Means and Variances
    • 10.4 Two-Sample Tests for Means and Variances
    • 10.5 Other Hypothesis Tests
    • 10.6 Analysis of Variance
    • 10.7 Sample Size and Power
    • Chapter Exercises
  • 11 Simple Linear Regression
    • 11.1 Basic Philosophy
    • 11.2 Estimation
    • 11.3 Model Utility and Inference
    • 11.4 Residual Analysis
    • 11.5 Other Diagnostic Tools
    • Chapter Exercises
  • 12 Multiple Linear Regression
    • 12.1 The Multiple Linear Regression Model
    • 12.2 Estimation and Prediction
    • 12.3 Model Utility and Inference
    • 12.4 Polynomial Regression
    • 12.5 Interaction
    • 12.6 Qualitative Explanatory Variables
    • 12.7 Partial F Statistic
    • 12.8 Residual Analysis and Diagnostic Tools
    • 12.9 Additional Topics
    • Chapter Exercises
  • 13 Resampling Methods
    • 13.1 Introduction
    • 13.2 Bootstrap Standard Errors
    • 13.3 Bootstrap Confidence Intervals
    • 13.4 Resampling in Hypothesis Tests
    • Chapter Exercises
  • 14 Categorical Data Analysis
  • 15 Nonparametric Statistics
  • 16 Time Series
  • A R Session Information
  • B GNU Free Documentation License
  • C History
  • D Data
    • D.1 Data Structures
    • D.2 Importing Data
    • D.3 Creating New Data Sets
    • D.4 Editing Data
    • D.5 Exporting Data
    • D.6 Reshaping Data
  • E Mathematical Machinery
    • E.1 Set Algebra
    • E.2 Differential and Integral Calculus
    • E.3 Sequences and Series
    • E.4 The Gamma Function
    • E.5 Linear Algebra
    • E.6 Multivariable Calculus
  • F Writing Reports with R
    • F.1 What to Write
    • F.2 How to Write It with R
    • F.3 Formatting Tables
    • F.4 Other Formats
  • G Instructions for Instructors
    • G.1 Generating This Document
    • G.2 How to Use This Document
    • G.3 Ancillary Materials
    • G.4 Modifying This Document
  • H RcmdrTestDrive Story
  • Bibliography
  • Index
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