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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Steven J Miller |

ISBN: | 1400885388 9781400885381 |

OCLC Number: | 987017971 |

Language Note: | In English. |

Description: | 1 online resource (xxiii, 727 pages). |

Contents: | 2.2 Set Theory Review2.2.1 Coding Digression; 2.2.2 Sizes of Infinity and Probabilities; 2.2.3 Open and Closed Sets; 2.3 Outcome Spaces, Events, and the Axioms of Probability; 2.4 Axioms of Probability; 2.5 Basic Probability Rules; 2.5.1 Law of Total Probability; 2.5.2 Probabilities of Unions; 2.5.3 Probabilities of Inclusions; 2.6 Probability Spaces and [sigma]-algebras; 2.7 Appendix: Experimentally Finding Formulas; 2.7.1 Product Rule for Derivatives; 2.7.2 Probability of a Union; 2.8 Summary; 2.9 Exercises; 3 Counting I: Cards; 3.1 Factorials and Binomial Coefficients Cover; Title; Copyright; CONTENTS; Note to Readers; How to Use This Book; I General Theory; 1 Introduction; 1.1 Birthday Problem; 1.1.1 Stating the Problem; 1.1.2 Solving the Problem; 1.1.3 Generalizing the Problem and Solution: Efficiencies; 1.1.4 Numerical Test; 1.2 From Shooting Hoops to the Geometric Series; 1.2.1 The Problem and Its Solution; 1.2.2 Related Problems; 1.2.3 General Problem Solving Tips; 1.3 Gambling; 1.3.1 The 2008 Super Bowl Wager; 1.3.2 Expected Returns; 1.3.3 The Value of Hedging; 1.3.4 Consequences; 1.4 Summary; 1.5 Exercises; 2 Basic Probability Laws; 2.1 Paradoxes 3.1.1 The Factorial Function3.1.2 Binomial Coefficients; 3.1.3 Summary; 3.2 Poker; 3.2.1 Rules; 3.2.2 Nothing; 3.2.3 Pair; 3.2.4 Two Pair; 3.2.5 Three of a Kind; 3.2.6 Straights, Flushes, and Straight Flushes; 3.2.7 Full House and Four of a Kind; 3.2.8 Practice Poker Hand: I; 3.2.9 Practice Poker Hand: II; 3.3 Solitaire; 3.3.1 Klondike; 3.3.2 Aces Up; 3.3.3 FreeCell; 3.4 Bridge; 3.4.1 Tic-tac-toe; 3.4.2 Number of Bridge Deals; 3.4.3 Trump Splits; 3.5 Appendix: Coding to Compute Probabilities; 3.5.1 Trump Split and Code; 3.5.2 Poker Hand Codes; 3.6 Summary; 3.7 Exercises 4 Conditional Probability, Independence, and Bayes' Theorem4.1 Conditional Probabilities; 4.1.1 Guessing the Conditional Probability Formula; 4.1.2 Expected Counts Approach; 4.1.3 Venn Diagram Approach; 4.1.4 The Monty Hall Problem; 4.2 The General Multiplication Rule; 4.2.1 Statement; 4.2.2 Poker Example; 4.2.3 Hat Problem and Error Correcting Codes; 4.2.4 Advanced Remark: Definition of Conditional Probability; 4.3 Independence; 4.4 Bayes' Theorem; 4.5 Partitions and the Law of Total Probability; 4.6 Bayes' Theorem Revisited; 4.7 Summary; 4.8 Exercises; 5 Counting II: Inclusion-Exclusion 5.1 Factorial and Binomial Problems5.1.1 "How many" versus "What's the probability"; 5.1.2 Choosing Groups; 5.1.3 Circular Orderings; 5.1.4 Choosing Ensembles; 5.2 The Method of Inclusion-Exclusion; 5.2.1 Special Cases of the Inclusion-Exclusion Principle; 5.2.2 Statement of the Inclusion-Exclusion Principle; 5.2.3 Justification of the Inclusion-Exclusion Formula; 5.2.4 Using Inclusion-Exclusion: Suited Hand; 5.2.5 The At Least to Exactly Method; 5.3 Derangements; 5.3.1 Counting Derangements; 5.3.2 The Probability of a Derangement; 5.3.3 Coding Derangement Experiments |

Series Title: | Princeton lifesaver study guide. |

Responsibility: | Steven J. Miller. |

More information: |

### Abstract:

## Reviews

*Editorial reviews*

Publisher Synopsis

"The breadth of the book's coverage and its clear, informal tone in addressing highly formal problems remind one of a friendly professor offering unlimited office hours, and the book will be a highly accessible supplement for students working through another, more conventional text. . . . [This is] a volume that deserves to be widely known in educational circles and will likely find its way to the shelves of practicing statisticians who wish to probe below the surface of fundamental theorems that they have learned by rote."--H. Van Dyke Parunak, Computing Reviews "I recommend the book to everyone who is studying and fascinated by statistics."--Singalakha Menziwa, Mathemafrica "Steven J. Miller's The Probability Lifesaver presents, as its subtitle claims, 'all the tools you need to understand chance' in a clear, straightforward manner. . . . For the students that have a good understanding of Calculus, the combination of the probability discussions along with the calculus behind these topics is very beneficial."--MAA Reviews Read more...

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