Probability with R

Provides a comprehensive introduction to probability with an emphasis on computing-related applications

This self-contained new and extended edition outlines a first course in probability applied to computer-related disciplines. As in the first edition, experimentation and simulation are favoured over mathematical proofs. The freely down-loadable statistical programming language R is used throughout the text, not only as a tool for calculation and data analysis, but also to illustrate concepts of probability and to simulate distributions. The examples in Probability with R: An Introduction with Computer Science Applications, Second Edition cover a wide range of computer science applications, including: testing program performance; measuring response time and CPU time; estimating the reliability of components and systems; evaluating algorithms and queuing systems.

Chapters cover: The R language; summarizing statistical data; graphical displays; the fundamentals of probability; reliability; discrete and continuous distributions; and more.

This second edition includes:

• improved R code throughout the text, as well as new procedures, packages and interfaces;

• updated and additional examples, exercises and projects covering recent developments of computing;

• an introduction to bivariate discrete distributions together with the R functions used to handle large matrices of conditional probabilities, which are often needed in machine translation;

• an introduction to linear regression with particular emphasis on its application to machine learning using testing and training data;

• a new section on spam filtering using Bayes theorem to develop the filters;

• an extended range of Poisson applications such as network failures, website hits, virus attacks and accessing the cloud;

• use of new allocation functions in R to deal with hash table collision, server overload and the general allocation problem.

The book is supplemented with a Wiley Book Companion Site featuring data and solutions to exercises within the book.

Primarily addressed to students of computer science and related areas, Probability with R: An Introduction with Computer Science Applications, Second Edition is also an excellent text for students of engineering and the general sciences. Computing professionals who need to understand the relevance of probability in their areas of practice will find it useful.

Autorentext

JANE M. HORGAN is Emeritus Professor of Statistics in the School of Computing, Dublin City University, Ireland. A Fellow of the Institute of Statisticians, she graduated in Statistics with a First Class Honours from University College Cork and completed postgraduate work at the London School of Economics and at London City University. Dr. Horgan has published extensively in statistics and computing.

Inhalt
Preface to the Second Edition xiii

Preface to the First Edition xvii

Acknowledgments xxi

About the Companion Website xxiii

I The R Language 1

1 Basics of R 3

1.1 What is R? 3

1.2 Installing R 4

1.3 R Documentation 4

1.4 Basics 5

1.5 Getting Help 6

1.6 Data Entry 7

1.7 Missing Values 11

1.8 Editing 12

1.9 Tidying Up 12

1.10 Saving and Retrieving 13

1.11 Packages 13

1.12 Interfaces 14

1.13 Project 16

2 Summarizing Statistical Data 17

2.1 Measures of Central Tendency 17

2.2 Measures of Dispersion 21

2.3 Overall Summary Statistics 24

2.4 Programming in R 25

2.5 Project 30

3 Graphical Displays 31

3.1 Boxplots 31

3.2 Histograms 36

3.3 Stem and Leaf 40

3.4 Scatter Plots 40

3.5 The Line of Best Fit 43

3.6 Machine Learning and the Line of Best Fit 44

3.7 Graphical Displays Versus Summary Statistics 49

3.8 Projects 53

II Fundamentals of Probability 55

4 Probability Basics 57

4.1 Experiments, Sample Spaces, and Events 58

4.2 Classical Approach to Probability 61

4.3 Permutations and Combinations 64

4.4 The Birthday Problem 71

4.5 Balls and Bins 76

4.6 R Functions for Allocation 79

4.7 Allocation Overload 81

4.8 Relative Frequency Approach to Probability 83

4.9 Simulating Probabilities 84

4.10 Projects 89

5 Rules of Probability 91

5.1 Probability and Sets 91

5.2 Mutually Exclusive Events 92

5.3 Complementary Events 93

5.4 Axioms of Probability 94

5.5 Properties of Probability 96

6 Conditional Probability 104

6.1 Multiplication Law of Probability 107

6.2 Independent Events 108

6.3 Independence of More than Two Events 110

6.4 The Intel Fiasco 113

6.5 Law of Total Probability 115

6.6 Trees 118

6.7 Project 123

7 Posterior Probability and Bayes 124

7.1 Bayes' Rule 124

7.2 Hardware Fault Diagnosis 131

7.3 Machine Learning and Classification 132

7.4 Spam Filtering 135

7.5 Machine Translation 137

8 Reliability 142

8.1 Series Systems 142

8.2 Parallel Systems 143

8.3 Reliability of a System 143

8.4 SeriesParallel Systems 150

8.5 The Design of Systems 153

8.6 The General System 158

III Discrete Distributions 161

9 Introduction to Discrete Distributions 163

9.1 Discrete Random Variables 163

9.2 Cumulative Distribution Function 168

9.3 Some Simple Discrete Distributions 170

9.4 Benford's Law 174

9.5 Summarizing Random Variables: Expectation 175

9.6 Properties of Expectations 180

9.7 Simulating Discrete Random Variables and Expectations 183

9.8 Bivariate Distributions 187

9.9 Marginal Distributions 189

9.10 Conditional Distributions 190

9.11 Project 194

10 The Geometric Distribution 196

10.1 Geometric Random Variables 198

10.2 Cumulative Distribution Function 203

10.3 The Quantile Function 207

10.4 Geometric Expectations 209

10.5 Simulating Geometric Probabilities and Expectations 210

10.6 Amnesia 217

10.7 Simulating Markov 219

10.8 Projects 224 **11 The Binomial Distribu...