Probability, Random Variables, Statistics, and Random Processes: Fundamentals & Applications (Hardcover)

Preface

Acknowledgments

About the companion website

Part I PROBABILITY

Chapter 1 Basic Concepts of Probability Theory

1.1 Statistical Regularity and Relative Frequency

1.2 Set Theory and Its Applications to Probability

1.3 The Axioms and Corollaries of Probability

1.4 Joint Probability and Conditional Probability

1.5 Statistically-Independent Events and Mutually-Exclusive Events

1.6 Law of Total Probability and Bayes’ Theorem

Chapter 2 Applications in Probability

2.1 Odds and Risk

2.2 Gambler’s Ruin Problem

2.3 Systems Reliability

2.4 Medical Diagnostic Testing

2.5 Bayesian Spam Filtering

2.6 Monty Hall Problem

2.7 Digital Transmission Error

2.8 How to Make the Best Choice Problem

2.9 The Viterbi Algorithm

2.10 All Eggs in One Basket

Chapter 3 Counting Methods and Applications

3.1 Basic Rules of Counting

3.2 Permutations and Combinations

3.3 Multinomial Counting

3.4 Special Arrangements and Selections

3.5 Applications

Part II RANDOM VARIABLES

Chapter 4 One Random Variable: Fundamentals

4.1 Types of Random Variables

4.2 The Cumulative Distribution Function

4.3 The Probability Mass Function

4.4 The Probability Density Function

4.5 Expected Values

4.6 Conditional Distributions

4.7 Functions of a Random Variable

4.8 Transform Methods

4.9 Upper Bounds on Probability

Chapter 5 Special Probability Distributions and Applications

5.1 Special Discrete Random Variables

5.2 Special Continuous Random Variables

5.3 Applications

Chapter 6 Multiple Random Variables

6.1 Pairs of Random Variables

6.2 The Joint Cumulative Distribution Function of Two Random Variables

6.3 The Joint Probability Mass Function of Two Random Variables

6.4 The Joint Probability Density Function of Two Random Variables

6.5 Expected Values of Functions of Two Random Variables

6.6 Independence of Two Random Variables

6.7 Correlation between Two Random Variables

6.8 Conditional Distributions

6.9 Distributions of Functions of Two Random Variables

6.10 Random Vectors

Chapter 7 The Gaussian Distribution

7.1 The Gaussian Random Variable

7.2 The Standard Gaussian Distribution

7.3 Bivariate Gaussian Random Variables

7.4 Jointly Gaussian Random Vectors

7.5 Sums of Random Variables

7.6 The Sample Mean

7.7 Approximating Distributions with the Gaussian Distribution

7.8 Probability Distributions Related to the Gaussian Distribution

Part III STATISTICS

Chapter 8 Descriptive Statistics

8.1 Overview of Statistics

8.2 Data Displays

8.3 Measures of Location

8.4 Measures of Dispersion

8.5 Measures of Shape

Chapter 9 Estimation

9.1 Parameter Estimation

9.2 Properties of Point Estimators

9.3 Maximum Likelihood Estimators

9.4 Bayesian Estimators

9.5 Confidence Intervals

9.6 Estimation of a Random Variable

9.7 Maximum A posteriori Probability Estimation

9.8 Minimum Mean Square Error Estimation

9.9 Linear Minimum Mean Square Error Estimation

9.10 Linea MMSE Estimation Using a Vector of Observations

Chapter 10 Hypothesis Testing

10.1 Significance Testing

10.2 Hypothesis Testing for Mean

10.3 Decision Tests

10.4 Bayesian Test

10.5 Neyman-Pearson Test

Part IV RANDOM PROCESSES

Chapter 11 Introduction to Random Processes

11.1 Classification of Random Processes

11.2 Characterization of Random Processes

11.3 Moments of Random Processes

11.4 Stationary Random Processes

11.5 Ergodic Random Processes

11.6 Gaussian Processes

11.7 Poisson Processes

Chapter 12 Analysis and Processing of Random Processes

12.1 Stochastic Continuity, Differentiation, and Integration

12.2 Power Spectral Density

12.3 Noise

12.4 Sampling of Random Signals

12.5 Optimum Linear Systems

Bibliography

Index