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Probability for Electrical and Computer Engineers

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ISBN-10: 084931884X

ISBN-13: 9780849318849

Edition: 2004

Authors: Charles W. Therrien, Murali Tummala

List price: $104.95
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Written specifically for electrical and computer engineers, this book presents an introduction to probability and random variables. It includes methods of probability that deal with computing the likelihood of uncertain events, useful to scientists and engineers who predict the outcome of experiments, extrapolate results from a small case to a larger one, and design systems that will perform optimally when the exact characteristics of the inputs are unknown. Electrical and computer engineers seeking solutions to practical problems will find it a valuable resource for the design of communication systems, control systems, military or medical sensing or monitoring systems, and computer…    
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Book details

List price: $104.95
Copyright year: 2004
Publisher: CRC Press LLC
Publication date: 1/23/2004
Binding: Hardcover
Pages: 328
Size: 7.00" wide x 10.25" long x 0.75" tall
Weight: 1.584
Language: English

The Analysis of Random Experiments
Probability in Electrical and Computer Engineering
Signal detection and classification
Speech modeling and recognition
Coding and data transmission
Computer networks
Outline of the Book
The Probability Model
The Algebra of Events
Basic operations
Representation of the sample space
Probability of Events
Defining probability
Statistical independence
Some Applications
Repeated independent trials
Problems involving counting
Network reliability
Conditional Probability and Bayes' Rule
Conditional probability
Event trees
Bayes' rule
More Applications
The binary communication channel
Measuring information and coding
Random Variables and Transformations
Discrete Random Variables
Common Discrete Probability Distributions
Bernoulli random variable
Binomial random variable
Geometric random variable
Poisson random variable
Discrete uniform random variable
Continuous Random Variables
Probabilistic description
More about the PDF
A relation to discrete random variables
Solving problems
Common Continuous Probability Density Functions
Uniform random variable
Exponential random variable
Gaussian random variable
CDF and PDF for Discrete and Mixed Random Variables
Discrete random variables
Mixed random variables
Fransformation of Random Variables
When the transformation is invertible
When the transformation is not invertible
When the transformation has discontinuities or flat regions
Instributions Conditioned on an Event
Optimal signal detection
Object classification
Expectation, Moments, and Generating Functions
Expectation of a Random Variable
Discrete random variable
Continuous random variable
Invariance of expectation
Properties of expectation
Expectation conditioned on an event
Meanents of a Distribution
Central moments
Properties of variance
Some higher-order moments
Generating Functions
The moment generating function
The probability generating function
Application: Entropy and Source Coding
Two and More Random Variables
Two Discrete Random Variables
The joint PMF
Independent random variables
Conditional PMFs for discrete random variables
Bayes' rule for discrete random variables
Two Continuous Random Variables
Joint distributions
Marginal PDFs: Projections of the joint density
Conditional PDFs: Slices of the joint density
Bayes' rule for continuous random variables
Expectation and Correlation
Correlation and covariance
Conditional expectation
Gaussian Random Variables
Multiple Random Variables
PDFs for multiple random variables
Sums of random variables
Sums of Some Common Random Variables
Bernoulli random variables
Geometric random variables
Exponential random variables
Gaussian random variables
Squared Gaussian random variables
Random Vectors
Cumulative distribution and density functions
Expectation and moments
Multivariate Gaussian density function
Transformations of random vectors
An Application to Signal Detection
Inequalities, Limit Theorems, and Parameter Estimation
Markov inequality
Chebyshev inequality
One-sided Chebyshev inequality
Other inequalities
Convergence and Limit Theorems
Laws of large numbers
Central limit theorem
Estimation of Parameters
Estimates and properties
Sample mean and variance
Maximum Likelihood Estimation
Application to Signal Estimation
Random Processes
Random Process
The ensemble
First and Second Moments of a Random Process
Autocorrelation and autocovariance functions
Cross-correlation function
Properties: Independence, Stationarity, and Ergodicity
Statistical independence
Strict sense stationarity
Wide sense stationarity
Properties of correlation functions
Time averages and ergodic random processes
Power Spectral Density
Properties of the power spectral density
Cross-power spectral density
White noise
An application
Noise Sources
Thermal noise
Quantization noise
Response of Linear Systems
Linear time-invariant system
Output mean
Cross-correlation functions and cross-power spectra
Autocorrelation function and power spectral density of system output
Response of linear systems: discrete case
Markov and Poisson Random Processes
The Poisson Model
Derivation of the Poisson model
The Poisson process
An application of the Poisson process: the random telegraph signal
Additional remarks about the Poisson process
Discrete-Time Markov Chains
Definitions and dynamic equations
Higher-order transition probabilities
Limiting state probabilities
Continuous-Time Markov Chains
Simple server system
Analysis of continuous-time Markov chains
Special condition for birth and death processes
Basic Queueing Theory
The single-server system
Little's formula
The single-server system with finite capacity
The multi-server system
Basic Combinatorics
The Rule of Product
The Unit Impulse
The Impulse