Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers, 3rd Edition

Contents

Features of this Text

Preface

1   Experiments, Models, and Probabilities

Getting Started with Probability

1.1   Set Theory

1.2   Applying Set Theory to Probability

1.3   Probability Axioms

1.4   Conditional Probability

1.5   Partitions and the Law of Total Probability

1.6   Independence

1.7   MATLAB

Problems

2   Sequential Experiments

2.1   Tree Diagrams

2.2   Counting Methods

2.3   Independent Trials

2.4   Reliability Analysis

2.5   MATLAB

Problems

3   Discrete Random Variables

3.1   Definitions

3.2   Probability Mass Function

3.3   Families of Discrete Random Variables

3.4   Cumulative Distribution Function (CDF)

3.5   Averages and Expected Value

3.6   Functions of a Random Variable

3.7   Expected Value of a Derived Random Variable

3.8   Variance and Standard Deviation

3.9   MATLAB

Problems

4   Continuous Random Variables

4.1   Continuous Sample Space

4.2   The Cumulative Distribution Function

4.3   Probability Density Function

4.4   Expected Values

4.5   Families of Continuous Random Variables

4.6   Gaussian Random Variables

4.7   Delta Functions, Mixed Random Variables

4.8   MATLAB

Problems

5   Multiple Random Variables

5.1   Joint Cumulative Distribution Function

5.2   Joint Probability Mass Function

5.3   Marginal PMF

5.4   Joint Probability Density Function

5.5   Marginal PDF

5.6   Independent Random Variables

5.7   Expected Value of a Function of Two Random Variables

5.8   Covariance, Correlation and Independence

5.9   Bivariate Gaussian Random Variables

5.10  Multivariate ...