Probability Theory

A Complete One-Semester Course

This book provides a systematic, self-sufficient and yet short presentation of the mainstream topics on introductory Probability Theory with some selected topics from Mathematical Statistics. It is suitable for a 10- to 14-week course for second- or third-year undergraduate students in Science, Mathematics, Statistics, Finance, or Economics, who have completed some introductory course in Calculus. There is a sufficient number of problems and solutions to cover weekly tutorials.

Contents:

• Probability

• Random Variables

• Joint Distributions

• Transformations of the Distributions

• Expectation of Random Variables

• Variance and Covariance

• Conditional Expectations

• Moment Generating Functions

• Analysis of Some Important Distributions

• Limit Theorems

• Statistical Inference: Point Estimation

• Statistical Inference: Interval Estimation

• Appendices:

  • Solutions for the Problems for Weeks 1–12
  • Sample Problems for Final Exams
  • Some Bonus Challenging Problems
  • Statistical Tables

Readership: Undergraduate students, teachers and lecturers in Mathematics and Statistics.

Key Features:

• This book is short and comprehensive
• The amount of material is exactly as is needed for a one-semester course
• There are enough problems with solutions to cover weekly tutorials
• Supplementary PDF files of presentation slides are provided for lecturers who adopt the textbook