Book description
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.
Table of contents
- Cover
- Preface to the Second Edition
- Preface to the First Edition
- Acknowledgments
- About the Companion Website
- Part I: The R Language
-
Part II: Fundamentals of Probability
-
4 Probability Basics
- 4.1 Experiments, Sample Spaces, and Events
- 4.2 Classical Approach to Probability
- 4.3 Permutations and Combinations
- 4.4 The Birthday Problem
- 4.5 Balls and Bins
- 4.6 R Functions for Allocation
- 4.7 Allocation Overload
- 4.8 Relative Frequency Approach to Probability
- 4.9 Simulating Probabilities
- 4.10 Projects
- Recommended Reading
- 5 Rules of Probability
- 6 Conditional Probability
- 7 Posterior Probability and Bayes
- 8 Reliability
-
4 Probability Basics
-
Part III: Discrete Distributions
-
9 Introduction to Discrete Distributions
- 9.1 Discrete Random Variables
- 9.2 Cumulative Distribution Function
- 9.3 Some Simple Discrete Distributions
- 9.4 Benford's Law
- 9.5 Summarizing Random Variables: Expectation
- 9.6 Properties of Expectations
- 9.7 Simulating Discrete Random Variables and Expectations
- 9.8 Bivariate Distributions
- 9.9 Marginal Distributions
- 9.10 Conditional Distributions
- 9.11 Project
- References
- 10 The Geometric Distribution
- 11 The Binomial Distribution
- 12 The Hypergeometric Distribution
-
13 The Poisson Distribution
- 13.1 Death by Horse Kick
- 13.2 Limiting Binomial Distribution
- 13.3 Random Events in Time and Space
- 13.4 Probability Density Function
- 13.5 Cumulative Distribution Function
- 13.6 The Quantile Function
- 13.7 Estimating Software Reliability
- 13.8 Modeling Defects In Integrated Circuits
- 13.9 Simulating Poisson Probabilities
- 13.10 Projects
- References
-
14 Sampling Inspection Schemes
- 14.1 Introduction
- 14.2 Single Sampling Inspection Schemes
- 14.3 Acceptance Probabilities
- 14.4 Simulating Sampling Inspection Schemes
- 14.5 Operating Characteristic Curve
- 14.6 Producer's and Consumer's Risks
- 14.7 Design of Sampling Schemes
- 14.8 Rectifying Sampling Inspection Schemes
- 14.9 Average Outgoing Quality
- 14.10 Double Sampling Inspection Schemes
- 14.11 Average Sample Size
- 14.12 Single Versus Double Schemes
- 14.13 Projects
-
9 Introduction to Discrete Distributions
- Part IV: Continuous Distributions
- Part V: Tailing Off
- Appendix A: Data: Examination Results
- Appendix B: The Line of Best Fit: Coefficient Derivations
- Appendix C: Variance Derivations
- Appendix D: Binomial Approximation to the Hypergeometric
- Appendix E: Normal Tables
- Appendix F: The Inequalities of Markov and Chebyshev
- Index to R Commands
- Index
- Postface
- End User License Agreement
Product information
- Title: Probability with R, 2nd Edition
- Author(s):
- Release date: January 2020
- Publisher(s): Wiley
- ISBN: 9781119536949
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