Probability Random Signals and Statistics

INTRODUCTION
Randomness, Random Signals and Systems
Probability and Random Processes
Typical Engineering Applications
Why Study Probability and Random Signals
Key Features of the Book
Rules for the Presentation
BASIC CONCEPTS IN PROBABILITY
Basics of Set Theory
Fundamental Concepts in Probability
Conditional Probability
Independent Events
Total Probability Theorem and Bayes' Rule
Combined Experiments and Bernoulli Trials
THE RANDOM VARIABLE
Concept of Random Variable
Cumulative Distribution Function
Probability Density Function
Uniform Distribution
Gaussian Distribution and Central Limit Theorem
Some Other Commonly Used Distributions
Expectation and Moments
Functions of a Random Variable
Conditional Distributions
Generation of Random Numbers
Determination of Distribution from Data
Characteristic Functions
MULTIPLE RANDOM VARIABLES
Joint Distribution Functions
Joint Density Function
Independence of Random Variables
Expectation and Moments
Relation between Two Random Variables
Uniform Distributions
Jointly Gaussian Random Variables
Functions of Random Variables
Conditional Distributions
INTRODUCTION TO STATISTICS
Introduction
Sample Mean and Sample Variance
Empirical Distributions
Statistical Inference
Parameter Estimation
Hypothesis Testing
Linear Regression and Curve Fitting
RANDOM PROCESSES
Concept of Random Process
Characterization of Random Processes
Classification of Random Processes
Correlation Functions
Properties of Autocorrelation Functions
Sample Mean and Sample Correlation Functions
Relationship between Two Random Processes
Properties of Crosscorrelation Functions
Gaussian Random Processes
POWER SPECTRAL DENSITY
Concept of Power Spectral Density
Properties of Power Spectral Density
White Noise
Power Spectrum Estimation
Cross-Power Spectrum
Power Spectrum in Laplace Domain
Some Facts about Fourier Transforms
LINEAR SYSTEMS WITH RANDOM INPUTS
Deterministic Linear Systems
Time-Domain Analysis
Frequency-Domain Analysis
Summary of Input-Output Relationships
Linear Systems with White Noise Input
Equivalent Noise Bandwidth
Output of a Linear System as a Gaussian Process
OPTIMAL LINEAR SYSTEMS
Introduction
Signal-to-Noise Ratio
The Matched Filter
The Wiener Filter
Plus each chapter includes a summary, additional examples, problems, computer exercises, and self-test problems with solutions.