We use cookies to enhance your experience on our website. By continuing to use our website, you are agreeing to our use of cookies. You can change your cookie settings at any time. Find out more
Cover

Probability, Statistics, and Random Signals

Charles Boncelet

Publication Date - February 2016

ISBN: 9780190200510

432 pages
Hardcover
7-1/2 x 9-1/4 inches

In Stock

Retail Price to Students: $159.99

A one-semester, student-friendly approach to the undergraduate Probability and Statistics course in electrical engineering

Description

Probability, Statistics, and Random Signals offers a comprehensive treatment of probability, giving equal treatment to discrete and continuous probability. The topic of statistics is presented as the application of probability to data analysis, not as a cookbook of statistical recipes. This student-friendly text features accessible descriptions and highly engaging exercises on topics like gambling, the birthday paradox, and financial decision-making.

Features

  • Comprehensive treatment of probability, giving equal treatment to discrete and continuous probability
  • Designed to be more student friendly than available texts
  • Exercises focusing on the topics as they are developed throughout the chapters

About the Author(s)

Charles Boncelet has a BS in Applied and Engineering Physics from Cornell University and an MS and PhD in Electrical Engineering and Computer Science from Princeton University. Since 1984, he has been employed at the University of Delaware. He is a Professor in the Electrical & Computer Engineering Department and has a joint appointment in the Computer & Information Science Department. He is currently Associate Chair of Undergraduate Studies in the ECE Department.

Boncelet has written approximately 100 research papers in journals and technical conferences on a variety of topics in signal processing, information theory, probability, and algorithms. He regularly teaches courses in probability and statistics, signal processing, and communications.
Boncelet is a senior member of the IEEE and a member of SIAM, Eta Kappa Nu, and the Delaware Academy of Science.

Reviews

"Probability, Statistics, and Random Signals seems to remedy most of the shortcomings I have found in other texts. It is well written, succinct, and engaging. The examples and problems are excellent."--Eddie Jacobs, University of Memphis

"This book is detail oriented, expresses concepts clearly, and is very good for electrical engineering students. It covers solid basic materials, reflects the current state of the discipline, and is factually sound."--JeongHee Kim, San Jose State University

Table of Contents

    PREFACE

    1 PROBABILITY BASICS
    1.1 What Is Probability?
    1.2 Experiments, Outcomes, and Events
    1.3 Venn Diagrams
    1.4 Random Variables
    1.5 Basic Probability Rules
    1.6 Probability Formalized
    1.7 Simple Theorems
    1.8 Compound Experiments
    1.9 Independence
    1.10 Example: Can S Communicate With D?
    1.10.1 List All Outcomes
    1.10.2 Probability of a Union
    1.10.3 Probability of the Complement
    1.11 Example: Now Can S Communicate With D?
    1.11.1 A Big Table
    1.11.2 Break Into Pieces
    1.11.3 Probability of the Complement
    1.12 Computational Procedures
    Summary
    Problems

    2 CONDITIONAL PROBABILITY
    2.1 Definitions of Conditional Probability
    2.2 Law of Total Probability and Bayes Theorem
    2.3 Example: Urn Models
    2.4 Example: A Binary Channel
    2.5 Example: Drug Testing
    2.6 Example: A Diamond Network
    Summary
    Problems

    3 A LITTLE COMBINATORICS
    3.1 Basics of Counting
    3.2 Notes on Computation
    3.3 Combinations and the Binomial Coefficients
    3.4 The Binomial Theorem
    3.5 Multinomial Coefficient and Theorem
    3.6 The Birthday Paradox and Message Authentication
    3.7 Hypergeometric Probabilities and Card Games
    Summary
    Problems

    4 DISCRETE PROBABILITIES AND RANDOM VARIABLES
    4.1 Discrete Random Variable and Probability Mass Functions
    4.2 Cumulative Distribution Functions
    4.3 Expected Values
    4.4 Moment Generating Functions
    4.5 Several Important Discrete PMFs
    4.5.1 Uniform PMF
    4.5.2 Geometric PMF
    4.5.3 The Poisson Distribution
    4.6 Gambling and Financial Decision Making
    Summary
    Problems

    5 MULTIPLE DISCRETE RANDOM VARIABLES
    5.1 Multiple Random Variables and PMFs
    5.2 Independence
    5.3 Moments and Expected Values
    5.3.1 Expected Values for Two Random Variables
    5.3.2 Moments for Two Random Variables
    5.4 Example: Two Discrete Random Variables
    5.4.1 Marginal PMFs and Expected Values
    5.4.2 Independence
    5.4.3 Joint CDF
    5.4.4 Transformations With One Output
    5.4.5 Transformations With Several Outputs
    5.4.6 Discussion
    5.5 Sums of Independent Random Variables
    5.6 Sample Probabilities, Mean, and Variance
    5.7 Histograms
    5.8 Entropy and Data Compression
    5.8.1 Entropy and Information Theory
    5.8.2 Variable Length Coding
    5.8.3 Encoding Binary Sequences
    5.8.4 Maximum Entropy
    Summary
    Problems
    6 BINOMIAL PROBABILITIES
    6.1 Basics of the Binomial Distribution
    6.2 Computing Binomial Probabilities
    6.3 Moments of the Binomial Distribution
    6.4 Sums of Independent Binomial Random Variables
    6.5 Distributions Related to the Binomial
    6.5.1 Connections Between Binomial and Hypergeometric Probabilities
    6.5.2 Multinomial Probabilities
    6.5.3 The Negative Binomial Distribution
    6.5.4 The Poisson Distribution
    6.6 Parameter Estimation for Binomial and Multinomial Distributions
    6.7 Alohanet
    6.8 Error Control Codes
    6.8.1 Repetition-by-Three Code
    6.8.2 General Linear Block Codes
    6.8.3 Conclusions
    Summary
    Problems

    7 A CONTINUOUS RANDOM VARIABLE
    7.1 A Continuous Random Variable and Its Density, Distribution Function, and Expected Values
    7.2 Example Calculations for a Single Random Variable
    7.3 Selected Continuous Distributions
    7.3.1 The Uniform Distribution
    7.3.2 The Exponential Distribution
    7.4 Conditional Probabilities for a Continuous Random Variable
    7.5 Discrete PMFs and Delta Functions
    7.6 Quantization
    7.7 A Final Word
    Summary
    Problems

    8 MULTIPLE CONTINUOUS RANDOM VARIABLES
    8.1 Joint Densities and Distribution Functions
    8.2 Expected Values and Moments
    8.3 Independence
    8.4 Conditional Probabilities for Multiple Random Variables
    8.5 Extended Example: Two Continuous Random Variables
    8.6 Sums of Independent Random Variables
    8.7 Random Sums
    8.8 General Transformations and the Jacobian
    8.9 Parameter Estimation for the Exponential Distribution
    8.10 Comparison of Discrete and Continuous Distributions
    Summary
    Problems

    9 THE GAUSSIAN AND RELATED DISTRIBUTIONS
    9.1 The Gaussian Distribution and Density
    9.2 Quantile Function
    9.3 Moments of the Gaussian Distribution
    9.4 The Central Limit Theorem
    9.5 Related Distributions
    9.5.1 The Laplace Distribution
    9.5.2 The Rayleigh Distribution
    9.5.3 The Chi-Squared and F Distributions
    9.6 Multiple Gaussian Random Variables
    9.6.1 Independent Gaussian Random Variables
    9.6.2 Transformation to Polar Coordinates
    9.6.3 Two Correlated Gaussian Random Variables
    9.7 Example: Digital Communications Using QAM
    9.7.1 Background
    9.7.2 Discrete Time Model
    9.7.3 Monte Carlo Exercise
    9.7.4 QAM Recap
    Summary
    Problems

    10 ELEMENTS OF STATISTICS
    10.1 A Simple Election Poll
    10.2 Estimating the Mean and Variance
    10.3 Recursive Calculation of the Sample Mean
    10.4 Exponential Weighting
    10.5 Order Statistics and Robust Estimates
    10.6 Estimating the Distribution Function
    10.7 PMF and Density Estimates
    10.8 Confidence Intervals
    10.9 Significance Tests and p-Values
    10.10 Introduction to Estimation Theory
    10.11 Minimum Mean Squared Error Estimation
    10.12 Bayesian Estimation
    Summary
    Problems

    11 GAUSSIAN RANDOM VECTORS AND LINEAR REGRESSION
    11.1 Gaussian Random Vectors
    11.2 Linear Operations on Gaussian Random Vectors
    11.3 Linear Regression
    11.3.1 Linear Regression in Detail
    11.3.2 Statistics of the Linear Regression Estimates
    11.3.3 Computational Issues
    11.3.4 Linear Regression Examples
    11.3.5 Extensions of Linear Regression
    Summary
    Problems

    12 HYPOTHESIS TESTING
    12.1 Hypothesis Testing: Basic Principles
    12.2 Example: Radar Detection
    12.3 Hypothesis Tests and Likelihood Ratios
    12.4 MAP Tests
    Summary
    Problems

    13 RANDOM SIGNALS AND NOISE
    13.1 Introduction to Random Signals
    13.2 A Simple Random Process
    13.3 Fourier Transforms
    13.4 WSS Random Processes
    13.5 WSS Signals and Linear Filters
    13.6 Noise
    13.6.1 Probabilistic Properties of Noise
    13.6.2 Spectral Properties of Noise
    13.7 Example: Amplitude Modulation
    13.8 Example: Discrete Time Wiener Filter
    13.9 The Sampling Theorem for WSS Random Processes
    13.9.1 Discussion
    13.9.2 Example: Figure 13.4
    13.9.3 Proof of the Random Sampling Theorem
    Summary
    Problems

    14 SELECTED RANDOM PROCESSES
    14.1 The Lightbulb Process
    14.2 The Poisson Process
    14.3 Markov Chains
    14.4 Kalman Filter
    14.4.1 The Optimal Filter and Example
    14.4.2 QR Method Applied to the Kalman Filter
    Summary
    Problems
    A COMPUTATION EXAMPLES
    A.1 Matlab
    A.2 Python
    A.3 R
    B ACRONYMS
    C PROBABILITY TABLES
    C.1 Tables of Gaussian Probabilities
    D BIBLIOGRAPHY
    INDEX