Probability with R: An Introduction with Computer Science Applications

ISBN-13: 9781119536949 / Angielski / Twarda / 2020 / 496 str.

Jane Horgan

Spis treści

Preface to the Second Edition xiiiPreface to the First Edition xviiAcknowledgments xxiAbout the Companion Website xxiiiI The R Language 11 Basics of R 31.1 What is R? 31.2 Installing R 41.3 R Documentation 41.4 Basics 51.5 Getting Help 61.6 Data Entry 71.7 Missing Values 111.8 Editing 121.9 Tidying Up 121.10 Saving and Retrieving 131.11 Packages 131.12 Interfaces 141.13 Project 162 Summarizing Statistical Data 172.1 Measures of Central Tendency 172.2 Measures of Dispersion 212.3 Overall Summary Statistics 242.4 Programming in R 252.5 Project 303 Graphical Displays 313.1 Boxplots 313.2 Histograms 363.3 Stem and Leaf 403.4 Scatter Plots 403.5 The Line of Best Fit 433.6 Machine Learning and the Line of Best Fit 443.7 Graphical Displays Versus Summary Statistics 493.8 Projects 53II Fundamentals of Probability 554 Probability Basics 574.1 Experiments, Sample Spaces, and Events 584.2 Classical Approach to Probability 614.3 Permutations and Combinations 644.4 The Birthday Problem 714.5 Balls and Bins 764.6 R Functions for Allocation 794.7 Allocation Overload 814.8 Relative Frequency Approach to Probability 834.9 Simulating Probabilities 844.10 Projects 895 Rules of Probability 915.1 Probability and Sets 915.2 Mutually Exclusive Events 925.3 Complementary Events 935.4 Axioms of Probability 945.5 Properties of Probability 966 Conditional Probability 1046.1 Multiplication Law of Probability 1076.2 Independent Events 1086.3 Independence of More than Two Events 1106.4 The Intel Fiasco 1136.5 Law of Total Probability 1156.6 Trees 1186.7 Project 1237 Posterior Probability and Bayes 1247.1 Bayes' Rule 1247.2 Hardware Fault Diagnosis 1317.3 Machine Learning and Classification 1327.4 Spam Filtering 1357.5 Machine Translation 1378 Reliability 1428.1 Series Systems 1428.2 Parallel Systems 1438.3 Reliability of a System 1438.4 Series-Parallel Systems 1508.5 The Design of Systems 1538.6 The General System 158III Discrete Distributions 1619 Introduction to Discrete Distributions 1639.1 Discrete Random Variables 1639.2 Cumulative Distribution Function 1689.3 Some Simple Discrete Distributions 1709.4 Benford's Law 1749.5 Summarizing Random Variables: Expectation 1759.6 Properties of Expectations 1809.7 Simulating Discrete Random Variables and Expectations 1839.8 Bivariate Distributions 1879.9 Marginal Distributions 1899.10 Conditional Distributions 1909.11 Project 19410 The Geometric Distribution 19610.1 Geometric Random Variables 19810.2 Cumulative Distribution Function 20310.3 The Quantile Function 20710.4 Geometric Expectations 20910.5 Simulating Geometric Probabilities and Expectations 21010.6 Amnesia 21710.7 Simulating Markov 21910.8 Projects 22411 The Binomial Distribution 22611.1 Binomial Probabilities 22711.2 Binomial Random Variables 22911.3 Cumulative Distribution Function 23311.4 The Quantile Function 23511.5 Reliability: The General System 23811.6 Machine Learning 24111.7 Binomial Expectations 24511.8 Simulating Binomial Probabilities and Expectations 24811.9 Projects 25412 The Hypergeometric Distribution 25512.1 Hypergeometric Random Variables 25712.2 Cumulative Distribution Function 26012.3 The Lottery 26212.4 Hypergeometric or Binomial? 26612.5 Projects 27313 The Poisson Distribution 27413.1 Death by Horse Kick 27413.2 Limiting Binomial Distribution 27513.3 Random Events in Time and Space 28113.4 Probability Density Function 28313.5 Cumulative Distribution Function 28713.6 The Quantile Function 28913.7 Estimating Software Reliability 29013.8 Modeling Defects in Integrated Circuits 29213.9 Simulating Poisson Probabilities 29313.10 Projects 29814 Sampling Inspection Schemes 29914.1 Introduction 29914.2 Single Sampling Inspection Schemes 30014.3 Acceptance Probabilities 30114.4 Simulating Sampling Inspection Schemes 30314.5 Operating Characteristic Curve 30814.6 Producer's and Consumer's Risks 31014.7 Design of Sampling Schemes 31114.8 Rectifying Sampling Inspection Schemes 31514.9 Average Outgoing Quality 31614.10 Double Sampling Inspection Schemes 31814.11 Average Sample Size 31914.12 Single Versus Double Schemes 32014.13 Projects 324IV Continuous Distributions 32515 Introduction to Continuous Distributions 32715.1 Introduction to Continuous Random Variables 32815.2 Probability Density Function 32815.3 Cumulative Distribution Function 33115.4 The Uniform Distribution 33215.5 Expectation of a Continuous Random Variable 33615.6 Simulating Continuous Variables 33816 The Exponential Distribution 34116.1 Modeling Waiting Times 34116.2 Probability Density Function of Waiting Times 34216.3 Cumulative Distribution Function 34416.4 Modeling Lifetimes 34716.5 Quantiles 34916.6 Exponential Expectations 35116.7 Simulating Exponential Probabilities and Expectations 35316.8 Amnesia 35616.9 Simulating Markov 36016.10 Project 36917 Queues 37017.1 The Single Server Queue 37017.2 Traffic Intensity 37117.3 Queue Length 37217.4 Average Response Time 37617.5 Extensions of the M/M/1 Queue 37817.6 Project 38218 The Normal Distribution 38318.1 The Normal Probability Density Function 38518.2 The Cumulative Distribution Function 38718.3 Quantiles 38918.4 The Standard Normal Distribution 39118.5 Achieving Normality: Limiting Distributions 39418.6 Projects 40519 Process Control 40719.1 Control Charts 40719.2 Cusum Charts 41119.3 Charts for Defective Rates 41219.4 Project 416V Tailing Off 41720 The Inequalities of Markov and Chebyshev 41920.1 Markov's Inequality 42020.2 Algorithm Runtime 42620.3 Chebyshev's Inequality 427Appendix A: Data: Examination Results 433Appendix B: The Line of Best Fit: Coefficient Derivations 437Appendix C: Variance Derivations 440Appendix D: Binomial Approximation to the Hypergeometric 446Appendix E: Normal Tables 448Appendix F: The Inequalities of Markov and Chebyshev 450Index to R Commands 453Index 457Postface

O autorze

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.