tailieunhanh - Grinstead and Snell’s Introduction to Probability

text is designed for an introductory probability course at the university level for sophomores, juniors, and seniors in mathematics, physical and social sciences, engineering, and computer science. It presents a thorough treatment of ideas and techniques necessary for a firm understanding of the subject. The text is also recommended for use in discrete probability courses. The material is organized so that the discrete and continuous probability discussions are presented in a separate, but parallel, manner. This organization does not emphasize an overly rigorous or formal view of probabililty and therefore offers some strong pedagogical value. Hence, the discrete discussions can. | Grinstead and Snell s Introduction to Probability The CHANCE Project1 Version dated 4 July 2006 1Copyright C 2006 Peter G. Doyle. This work is a version of Grinstead and Snell s Introduction to Probability 2nd edition published by the American Mathematical Society Copyright C 2003 Charles M. Grinstead and J. Laurie Snell. This work is freely redistributable under the terms of the GNU Free Documentation License. To our wives and in memory of Reese T. Prosser Contents Preface vii 1 Discrete Probability Distributions 1 Simulation of Discrete Probabilities. 1 Discrete Probability Distributions. 18 2 Continuous Probability Densities 41 Simulation of Continuous Probabilities. 41 Continuous Density Functions. 55 3 Combinatorics 75 Permutations. 75 Combinations. 92 Card 4 Conditional Probability 133 Discrete Conditional Continuous Conditional 5 Distributions and Densities 183 Important Important Densities .205 6 Expected Value and Variance 225 Expected Variance of Discrete Random Continuous Random 7 Sums of Random Variables 285 Sums of Discrete Random Variables . 285 Sums of Continuous Random Variables . 291 8 Law of Large Numbers 305 Discrete Random Variables . 305 Continuous Random