CooperMcGillem

PapoulisPillai

GrinsteadSnell

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 NonDeterministic Processes
Stationary and NonStationary Processes
Ergodic and NonErgodic 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 Secondorder 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
InputOutput Cross Spectral Density




Ch. 9 – Optimum Linear Systems:
Introduction
Criteria
Restrictions
Optimization by Parameter Adjustment
Maximizing SignalToNoiseRatio
Minimizing Mean Square Error



