"Now available in a fully revised and updated new edition, this well-established textbook provides a straightforward introduction to the theory of probability. Topics covered include conditional probability, independence, discrete and continuous random variables, basic combinatorics, generating functions and limit theorems, and an introduction to Markov chains. This edition includes an elementary approach to martingales and the theory of Brownian motion, which supply the cornerstones for many topics in modern financial mathematics such as option and derivative pricing. The text is accessible to undergraduate students, and provides numerous worked examples and exercises to help build the important skills necessary for problem solving."--BOOK JACKET

Introduction --

App.

Review of Elementary Mathematical Prerequisites --

1.

Probability --

2.

Conditional Probability and Independence --

3.

Counting --

4.

Random Variables: Distribution and Expectation --

5.

Random Vectors: Independence and Dependence --

6.

Generating Functions and Their Applications --

7.

Continuous Random Variables --

8.

Jointly Continuous Random Variables --

9.

Markov Chains --

App.

Solutions and Hints for Selected Exercises and Problems