Paolella Marc S. Fundamental Probability. A Computational Approach

John Wiley & Sons, 2006. — 486 p. — ISBN: 978-0-470-02594-9.Like many branches of science, probability and statistics can be effectively taught and appreciated at many mathematical levels. This book is the first of two on probability, and designed to accompany a course aimed at students who possess a basic command of freshman calculus and some linear algebra, but with no previous exposure to probability. It follows the more or less traditional ordering of subjects at this level, though with greater scope and often more depth, and stops with multivariate transformations. The second book, referred to as Volume II, continues with more advanced topics, including (i) a detailed look at sums of random variables via exact and approximate numeric inversion of moment generating and characteristic functions, (ii) a discussion of more advanced distributions including the stable Paretian and generalized hyperbolic, and (iii) a detailed look at noncentral distributions, quadratic forms and ratios of quadratic forms.A subsequent book will deal with the subject of statistical modeling and extraction of information from data. In principle, such prerequisites render the books appropriate for upper division undergraduates in a variety of disciplines, though the amount of material and, in some topics covered, the depth and use of some elements from advanced calculus, make the books especially suited for students with more focus and mathematical maturity, such as undergraduate math majors, or beginning graduate students in statistics, finance or economics, and other fields which use the tools of probability and statistical methodology.Basic Probability
Combinatorics
Probability spaces and counting
Symmetric spaces and conditioning
Discrete Random Variables
Univariate random variables
Multivariate random variables
Sums of random variables
Continuous Random Variables
Continuous univariate random variables
Joint and conditional random variables
Multivariate transformations
Appendices
Calculus review
Notation tables
Distribution tables