An Introduction to Probability

With MATHEMATICA®

By: Edward P C Kao

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eText | 17 January 2025 | Edition Number 2

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This edition covers the standard materials to be expected in a course from a calculus-based course in probability. A new chapter is added to cover exchangeability, embedding, and Monte Carlo simulation.

Contents:

Preface to the First Edition
Preface to the Second Edition
Notations and Abbreviations
Permutation and Combination
Axioms of Probability
Conditional Probability
Random Variables
Discrete Random Variables
Continuous Random Variables
Jointly Distributed Random Variables
Dependence and More on Expectations
Limit Theorems
Exchangeability, Embedding, and Monte Carlo
A Terse Introduction to Mathematica
Answers to Odd-Numbered Problems
Index

Readership: Undergraduate students specialising in mathematics, engineering, computer science, actuarial science and business.

Edward P C Kao is a Professor of Mathematics at the University of Houston. He received his PhD from Stanford and did his post-doctoral work at Yale. He was a Visiting Scientist at the Operations Research Center at MIT during 9/97–5/98.Professor Kao served as an Associate Editor of Operation Research, 1/83–12/87; Associate Editor of Inform Journal on Computing, 1/927/96, and the Area Editor in Computational Probability and Analysis of Inform Journal on Computing, 8/96–1/07.Professor Kao is the author of An Introduction of Stochastic Processes, Duxbury,1997; China Machine Press, 2002, and Dover 2019. He served as consulting statistician for various companies and legal institutions.