Intro
Preface
Overview
Chapter Descriptions
Contents
Part I Concepts of Probability Theory
1 Introduction
1.1 Set Theory
1.2 Set Operations
1.3 Sample Space and Events
1.4 Probability Axioms
1.5 Probability of the Equally Likely Outcomes
1.6 Conditional Probability and Bayes' Theory
1.7 Problems
2 Continuous Random Variables
2.1 The Probability Distribution Function (PDF)
2.2 The Probability Density Function (PDF)
2.3 Expected Value and Variance
2.4 Common Continuous Probability Distribution Functions
2.4.1 Uniform Distribution

2.4.2 Normal (Gaussian) Distribution
2.4.3 Exponential Distribution
2.4.4 Gamma Distribution
2.5 Problems
3 Discrete Random Variables
3.1 The Probability Distribution Function (PDF)
3.2 The Probability Density Function (PDF)
3.3 Expected Value and Variance
3.4 Common Discrete Probability Distribution Functions
3.4.1 Uniform Distribution
3.4.2 Bernoulli Distribution
3.4.3 Binomial Distribution
3.4.4 Geometric Distribution
3.4.5 The Memoryless Property of the Geometric Distribution
3.4.6 Poisson Distribution
3.5 The Mixed Probability Distributions

3.6 Problems
4 Multiple Random Variables
4.1 The Joint Probability Distribution Function
4.2 The Joint Probability Density Function
4.3 Marginal Probability Functions
4.3.1 Marginal Probability Distribution Function
4.3.2 Marginal Probability Density Function
4.4 Conditional Probability and Statistical Independence
4.5 Functions of Random Variables
4.5.1 Y=aX+b, a>0, Continuous Random Variables
4.5.2 Y=aX+b, a0, Discrete Random Variables
4.5.4 Y=X2

4.5.5 Sum of Two Statistically Independent Continuous Random Variables, Z=X+Y
4.5.6 Sum of Two Statistically Independent Discrete Random Variables, Z=X+Y
4.5.7 Z=XY
4.5.8 Z=XY
4.5.9 Central Limit Theorem
4.6 Problems
5 Statistical Analysis of Random Variables
5.1 Statistical Analysis of One Random Variable
5.1.1 Expected Value and Mean
5.1.2 Variance and Standard Deviation
5.2 Moment Generating Functions
5.2.1 Maclaurin Series
5.2.2 Characteristic Function
5.3 Statistical Analysis of Multiple Random Variables
5.3.1 Normalized Joint Moments

5.3.2 Joint Moments Around the Expected Values
5.3.3 Expected Operations of Functions of Random Variables
5.4 Problems
Part II Random Processes
6 Random Processes
6.1 Random Processes
6.1.1 Probability Functions Associated with a Random Process
6.1.2 Classification of Random Processes
6.2 Correlation Functions
6.2.1 Autocorrelation Function, RXX(t1,t2)
6.2.2 Cross-Correlation Function, RXY(t1,t2)
6.3 Covariance Functions
6.3.1 Autocovariance Function, CXX(t1,t2)
6.3.2 Cross-covariance Function, CXX(t1,t2)
6.4 Gaussian Random Process