# Textbook/Reference Cross Reference Table

 Cooper-McGillem Papoulis-Pillai Grinstead-Snell Gray Ch. 1 Introduction to Probability: Engineering Applications Random Experiments and Events Defining Probability Relative Frequency Axiomatic Independence Combined Events Bernoulli Trials Part I Probability and Random Variables 1 The Meaning of Probability 2 The Axioms of Probability 3 Repeated trials 1 Discrete Probability Distributions 2 Continuous Probability Densities 3 Combinatorics 9 Bernoulli Trials 1 Introduction 2 Probability 2.1 Introduction 2.2 Spinning pointers and flipping coins 2.3 Probability spaces 2.4 Discrete probability spaces 2.5 Continuous probability spaces 2.6 Independence 2.7 Elementary conditional probability Ch. 2 - Random Variables Distribution and Density Functions Mean Values and Moments Gaussian Other Distributions Conditional Distribution and Density Functions 4 The Concept of a Random Variable 4 Conditional Probability 5 Distributions and Densities 5.1 Important Distributions 5.2 Important Densities 3 Random variables, vectors, and processes 4 Expectation and averages A.c Common distributions Ch. 3 - Multiple Random Variables:  Two Random Variables Conditional Probability – revisited Statistical Independence PDF of Functions of Two Random Variables The Characteristic Function 5 Functions of a random Variable 6 Two random Variables 7 Sequences of Random Variables 6 Expected Value and Variance 7 Sums of Random Variables 8 Law of Large Numbers 9 Central Limit Theorem Ch. 4 – Elements of Statistics:  Introduction Sampling Theory Sampling Distributions and Confidence Hypothesis Testing Curve Fitting and Linear Regression Correlation Between Two Sets of Data 8 Statistics Ch. 5 – Random Processes:  Introduction Continuous and Discrete Random Processes Deterministic and Non-Deterministic Processes Stationary and Non-Stationary Processes Ergodic and Non-Ergodic Processes Measurement of Process Parameters Smoothing Data: A Moving Average Filter Part II Stochastic Processes 9   General Concepts 10 Random Walks and Other Applications Ch. 6 – Correlation Functions:  Introduction Autocorrelation of a Binary Process Autocorrelation Functions Cross Correlation Functions Correlation Matrices of Sampled Functions Ch. 7 – Spectral Density:  Introduction The Fourier Transform Properties of the Spectral density The Complex Frequency Plane Mean Square Values Autocorrelation The Periodogram 11 Spectral Representation 12 Spectrum Estimation 5 Second-order theory Ch. 8 – Linear Systems:  Introduction Time domain Mean and Mean Square Value of System Output Autocorrelation of System Output Cross Correlation between Input and Output Analysis in the Frequency Domain Spectral Density at the System Output Input-Output Cross Spectral Density 13 Mean Square Estimation Ch. 9 – Optimum Linear Systems:  Introduction Criteria Restrictions Optimization by Parameter Adjustment Maximizing Signal-To-Noise-Ratio Minimizing Mean Square Error