## Probability and Random Variables: A Beginner's GuideThis concise introduction to probability theory is written in an informal, tutorial style with concepts and techniques defined and developed as necessary. After an elementary discussion of chance, Stirzaker sets out the central and crucial rules and ideas of probability including independence and conditioning. Counting, combinatorics, and the ideas of probability distributions and densities follow. Later chapters present random variables and examine independence, conditioning, covariance, and functions of random variables, both discrete and continuous. The final chapter considers generating functions and applies this concept to practical problems including branching processes, random walks, and the central limit theorem. Examples, demonstrations, and exercises are used throughout to explore the ways in which probability is motivated by, and applied to, real life problems in science, medicine, gaming and other subjects of interest. Essential proofs of important results are included. Assuming minimal prior technical knowledge on the part of the reader, this book is suitable for students taking introductory courses in probability and will provide a solid foundation for more advanced courses in probability and statistics. It is also a valuable reference to those needing a working knowledge of probability theory and will appeal to anyone interested in this endlessly fascinating and entertaining subject. |

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### Contents

The rules of probability | 31 |

Counting and gambling | 93 |

trials samples and approximation | 129 |

B Random Variables | 185 |

Jointly distributed random variables | 238 |

Generating functions | 309 |

Hints and solutions for selected exercises and problems | 336 |

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### Common terms and phrases

1n fact 1n particular addition rule answer approximation balls Bernoulli trials binomial distribution calculate cards chance chapter choose coin shows conditional expectation conditional probability consider continuous random variables course defined Definition denote density f(x dice discrete random variables distribution function distribution p(x equally event Example Exercises for section expected value experiment fair coin Figure Find the density Find the distribution Find the probability gambler gambler's ruin geometric distribution given gives Hence ideas important independent integer intuitively joint density joint distribution key rule lottery mean Moivre negative binomial distribution normal density number of flips occurs odds pairs parameter partition rule Poisson distribution possible outcomes probability distribution probability generating function problem result Rod wins roll sample space scores sequence shows a head simple Solution Suppose symmetry tails theorem uniform variance yields

### References to this book

Numerical Methods for Structured Markov Chains Dario A. Bini,Guy Latouche,Beatrice Meini No preview available - 2005 |

Mathematics for Finance: An Introduction to Financial Engineering Marek Capiński,Tomasz Zastawniak No preview available - 2003 |