## Introduction to ProbabilityThis text is designed for an introductory probability course at the university level for undergraduates in mathematics, the physical and social sciences, engineering, and computer science. It presents a thorough treatment of probability ideas and techniques necessary for a firm understanding of the subject. |

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Great book, and freely and legally available online from the authors.

### Contents

Discrete Probability Distributions | 1 |

Continuous Probability Densities | 41 |

Combinatorics | 75 |

Conditional Probability | 133 |

Distributions and Densities | 183 |

Expected Value and Variance | 225 |

Sums of Random Variables | 285 |

Law of Large Numbers | 305 |

Central Limit Theorem | 325 |

Generating Functions | 365 |

Markov Chains | 405 |

Random Walks | 471 |

Appendices | 499 |

### Common terms and phrases

approximately assign assume balls bar graph Bernoulli trials binomial distribution branching process calculate called cards Central Limit Theorem Chebyshev's Inequality choose chosen at random coin is tossed consider continuous random variable cumulative distribution function deck defined denote density function dice discrete random variables distribution with parameter dollars equal equation ergodic chain estimate event Example Exercise expected number expected value experiment exponential density fair coin Find the probability finite formula fx(x gambler given independent random variables independent trials process interval 0,1 Large Numbers Law of Large Markov chain Mathematics mean normally distributed number of heads obtain occurs offspring pair Pascal percent permutation play player Poisson distribution possible outcomes probability vector problem proof queue random numbers random walk real number rolls sample space Show simulation subset Suppose Table transition matrix variance a2 Write a program