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Introduction to Probability and Statistics Using R

Name: Introduction to Probability and Statistics Using R
ISBN: 978-0-557-24979-4

By G. Jay Kerns

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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