Probability Theory

A Complete One-Semester Course

By: Nikolai Dokuchaev

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eText | 12 June 2015

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224 Pages

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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.

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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