Introduction to Probability, Second Edition, 2nd Edition

Contents

Preface

1    Probability and counting

1.1    Why study probability?

1.2    Sample spaces and Pebble World

1.3    Naive definition of probability

1.4    How to count

1.5    Story proofs

1.6    Non-naive definition of probability

1.7    Recap

1.8    R

1.9    Exercises

2    Conditional probability

2.1    The importance of thinking conditionally

2.2    Definition and intuition

2.3    Bayes’ rule and the law of total probability

2.4    Conditional probabilities are probabilities

2.5    Independence of events

2.6    Coherency of Bayes’ rule

2.7    Conditioning as a problem-solving tool

2.8    Pitfalls and paradoxes

2.9    Recap

2.10  R

2.11  Exercises

3    Random variables and their distributions

3.1    Random variables

3.2    Distributions ...