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.

• 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
• 2.2 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
• 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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