Introduction to Probability and Statistics Using R

1 Introduction to Probabilityand Statistics UsingRG. Jay KernsFirst EditioniiIPSUR: Introduction to Probability and Statistics UsingRCopyright 2011 G. Jay KernsISBN: 978-0-557-24979-4 Permission is granted to copy, distribute and/or modify this document under the termsof the GNU Free Documentation License, Version or any later version published bythe Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and noBack-Cover Texts. A copy of the license is included in the section entitled GNU FreeDocumentation License .Date: August 12, 2011 ContentsPrefaceviiList of FiguresxiiiList of Tablesxv1 An Introduction to Probability and Probability .

2 Statistics ..1 Chapter Exercises ..22 An Introduction Downloading and InstallingR.. Communicating withR.. BasicROperations and Concepts .. Getting Help .. External Resources .. Other Tips ..15 Chapter Exercises ..163 Data Types of Data .. Features of Data Distributions .. Descriptive Statistics .. Exploratory Data Analysis .. Multivariate Data and Data Frames .. Comparing Populations ..46 Chapter Exercises ..534 Sample Spaces .. Events .. Model Assignment .. Properties of Probability .. Counting Methods .. Conditional Probability .. Independent Events.

3 Bayes Rule .. Random Variables .. 103 Chapter Exercises .. 107iiiivCONTENTS5 Discrete Discrete Random Variables .. The Discrete Uniform Distribution .. The Binomial Distribution .. Expectation and Moment Generating Functions .. The Empirical Distribution .. Other Discrete Distributions .. Functions of Discrete Random Variables .. 133 Chapter Exercises .. 1356 Continuous Continuous Random Variables .. The Continuous Uniform Distribution .. The Normal Distribution .. Functions of Continuous Random Variables .. Other Continuous Distributions.

4 153 Chapter Exercises .. 1587 Multivariate Joint and Marginal Probability Distributions .. Joint and Marginal Expectation .. Conditional Distributions .. Independent Random Variables .. Exchangeable Random Variables .. The Bivariate Normal Distribution .. Bivariate Transformations of Random Variables .. Remarks for the Multivariate Case .. The Multinomial Distribution .. 182 Chapter Exercises .. 1848 Sampling Simple Random Samples .. Sampling from a Normal Distribution .. The Central Limit Theorem .. Sampling Distributions of Two-Sample Statistics .

5 Simulated Sampling Distributions .. 193 Chapter Exercises .. 1969 Point Estimation .. Confidence Intervals for Means .. Confidence Intervals for Differences of Means .. Confidence Intervals for Proportions .. Confidence Intervals for Variances .. Fitting Distributions .. Sample Size and Margin of Error .. Other Topics .. 220 Chapter Exercises .. 221 CONTENTSv10 Hypothesis Introduction .. Tests for Proportions .. One Sample Tests for Means and Variances .. Two-Sample Tests for Means and Variances .. Other Hypothesis Tests .. Analysis of Variance.

6 Sample Size and Power .. 237 Chapter Exercises .. 23911 Simple Linear Basic Philosophy .. Estimation .. Model Utility and Inference .. Residual Analysis .. Other Diagnostic Tools .. 266 Chapter Exercises .. 27412 Multiple Linear The Multiple Linear Regression Model .. Estimation and Prediction .. Model Utility and Inference .. Polynomial Regression .. Interaction .. Qualitative Explanatory Variables .. PartialFStatistic .. Residual Analysis and Diagnostic Tools .. Additional Topics .. 301 Chapter Exercises .. 30513 Resampling Introduction .

7 Bootstrap Standard Errors .. Bootstrap Confidence Intervals .. Resampling in Hypothesis Tests .. 316 Chapter Exercises .. 31914 Categorical Data Analysis32115 Nonparametric Statistics32316 Time Series325 ARSession Information327B GNU Free Documentation License329C History337D Data Structures .. Importing Data .. Creating New Data Sets .. Editing Data .. Exporting Data .. Reshaping Data .. 347E Mathematical Set Algebra .. Differential and Integral Calculus .. Sequences and Series .. The Gamma Function .. Linear Algebra .. Multivariable Calculus.

8 357F Writing Reports What to Write .. How to Write It withR.. Formatting Tables .. Other Formats .. 365G Instructions for Generating This Document .. How to Use This Document .. Ancillary Materials .. Modifying This Document .. 370 HRcmdrTestDriveStory371 Bibliography377 PrefaceThis book was expanded from lecture materials I use in a one semester upper-divisionundergraduate course entitledProbability and Statisticsat Youngstown State lecture materials, in turn, were based on notes that I transcribed as a graduate stu-dent at Bowling Green State University. The course for which the materials were writtenis 50-50 Probability and Statistics , and the attendees include mathematics, engineering,and computer science majors (among others).

9 The catalog prerequisites for the courseare a full year of book can be subdivided into three basic parts. The first part includes the in-troductions and elementarydescriptive Statistics ; I want the students to be knee-deep indata right out of the gate. The second part is the study ofprobability, which begins atthe basics of sets and the equally likely model, journeys past discrete/continuous randomvariables, and continues through to multivariate distributions. The chapter on samplingdistributions paves the way to the third part, which isinferential Statistics . This last partincludes point and interval estimation, hypothesis testing, and finishes with introductionsto selected topics in applied usually only have time in one semester to cover a small subset of this book.

10 I cover thematerial in Chapter 2 in a class period that is supplemented by a take-home assignmentfor the students. I spend a lot of time on Data Description, Probability , Discrete, andContinuous Distributions. I mention selected facts from Multivariate Distributions inpassing, and discuss the meaty parts of Sampling Distributions before moving right alongto Estimation (which is another chapter I dwell on considerably). Hypothesis Testinggoes faster after all of the previous work, and by that time the end of the semester is insight. I normally choose one or two final chapters (sometimes three) from the remainingto survey, and regret at the end that I did not have the chance to cover an attempt to be correct I have included material in this book which I wouldnormally not mention during the course of a standard lecture.