Book contents
- Frontmatter
- Contents
- Preface to the Second Edition
- 0 Introduction
- 1 Probability
- 2 Conditional Probability and Independence
- 3 Counting
- 4 Random Variables: Distribution and Expectation
- 5 Random Vectors: Independence and Dependence
- 6 Generating Functions and Their Applications
- 7 Continuous Random Variables
- 8 Jointly Continuous Random Variables
- 9 Markov Chains
- Appendix: Solutions and Hints for Selected Exercises and Problems
- Further Reading
- Index of Notation
- Index
0 - Introduction
Published online by Cambridge University Press: 05 September 2012
- Frontmatter
- Contents
- Preface to the Second Edition
- 0 Introduction
- 1 Probability
- 2 Conditional Probability and Independence
- 3 Counting
- 4 Random Variables: Distribution and Expectation
- 5 Random Vectors: Independence and Dependence
- 6 Generating Functions and Their Applications
- 7 Continuous Random Variables
- 8 Jointly Continuous Random Variables
- 9 Markov Chains
- Appendix: Solutions and Hints for Selected Exercises and Problems
- Further Reading
- Index of Notation
- Index
Summary
A life which included no improbable events would be the real statistical improbability.
Poul AndersonIt is plain that any scientist is trying to correlate the incoherent body of facts confronting him with some definite and orderly scheme of abstract relations, the kind of scheme which he can borrow only from mathematics.
G. H. HardyThis chapter introduces the basic concepts of probability in an informal way. We discuss our everyday experience of chance, and explain why we need a theory and how we start to construct one. Mathematical probability is motivated by our intuitive ideas about likelihood as a proportion in many practical instances. We discuss some of the more common questions and problems in probability, and conclude with a brief account of the history of the subject.
Chance
My only solution for the problem of habitual accidents is to stay in bed all day. Even then, there is always the chance that you will fall out.
Robert BenchleyIt is not certain that everything is uncertain.
Blaise PascalYou can be reasonably confident that the sun will rise tomorrow, but what it will be shining on is a good deal more problematical. In fact, the one thing we can be certain of is that uncertainty and randomness are unavoidable aspects of our experience.
At a personal level, minor ailments and diseases appear unpredictably and are resolved not much more predictably. Your income and spending are subject to erratic strokes of good or bad fortune.
- Type
- Chapter
- Information
- Elementary Probability , pp. 1 - 23Publisher: Cambridge University PressPrint publication year: 2003