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.