## An introduction to probability theory and its applicationsMajor changes in this edition include the substitution of probabilistic arguments for combinatorial artifices, and the addition of new sections on branching processes, Markov chains, and the De Moivre-Laplace theorem. |

### What people are saying - Write a review

#### LibraryThing Review

User Review - redgiant - LibraryThingIf you were to lock me up for a year and allow only one book for the whole time, this is the book I would take with me. The way each problem is treated is delightful. The book is slightly dated and so ... Read full review

### Contents

The Exponential and the Uniform Densities | 1 |

Densities Convolutions | 3 |

The Exponential Density | 8 |

Copyright | |

174 other sections not shown

### Other editions - View all

### Common terms and phrases

applies arbitrary argument assume atoms Baire functions Borel sets bounded central limit theorem common distribution conditional density consider continuous function converges convolution coordinate variables defined definition denote depends derived distributed uniformly distribution F distribution function equals event example exists exponential distribution finite interval fixed follows formula given hence identity implies independent random variables independent variables inequality infinitely divisible integral ladder Laplace transform large numbers law of large lemma length limit theorem linear Markov Markovian martingale matrix measure monotone mutually independent normal density normal distribution notation obvious operator parameter Poisson process positive probabilistic probability distribution probability space problem proof prove random walk renewal equation renewal process result sample space satisfying semi-group sequence solution stable distribution stationary stochastic processes sufficiently symmetric tends theory uniform distribution unique vanishes variance vector zero expectation