Introduction to Probability

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American Mathematical Soc., 1998 - Mathematics - 510 pages
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Probability theory began in seventeenth century France when the two great French mathematicians, Blaise Pascal and Pierre de Fermat, corresponded over two problems from games of chance. Problems like those Pascal and Fermat solved continued to influence such early researchers as Huygens, Bernoulli and DeMoivre in establishing a mathematical theory of probability. Today, probability theory is a well-established branch of mathematics that finds applications in every area of scholarly activity from music to physics, and in daily experience from weather prediction to predicting the risks of new medical treatments. This text is designed for an introductory probability course taken by sophomores, juniors and seniors in mathematics, the physical and social sciences, engineering and computer science. It presents a thorough treatment of probability ideas and techniques necessary for a form understanding of the subject. The text can be used in a variety of course lengths, levels, and areas of emphasis. For use in a standard one-term course, in which both discrete and continuous probability is covered, students should have taken as a prerequisite two terms of calculus, including an introduction to multiple integrals. In order to cover Chapter 11, which contains material on Markov chains, some knowledge of matrix theory is necessary. The text can also be used in a discrete probability course. The material has been organized in such a way that the discrete and continuous probability discussions are presented in a separate, but parallel, manner. This organization dispels an overly rigorous or formal view of probability and offers some strong pedagogical value in that the discrete discussions can sometimes serve to motivate the more abstract continuous probability discussions. For use in a discrete probability course, students should have taken one term of calculus as a prerequisite. Very little computing background is assumed or necessary in order to obtain full benefits from the use of the computing material and examples in the text. All of the programs that are used in the text have been written in each of the languages TrueBASIC, Maple and Mathematica.
 

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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
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Probability Models
John Haigh
Limited preview - 2002
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