Probability Theory And Mathematical Statistics

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 De Moivre 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. These Chapters notes are designed for an introductory probability course taken by social sciences, engineering, and computer science English-speaking students. The course presents a thorough treatment of probability ideas and techniques necessary for a firm understanding of the subject. 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 the material on Markov chains, some knowledge of matrix