Probability and Random Processes

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John Wiley & Sons, Jul 28, 2006 - Mathematics - 420 pages
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A resource for probability AND random processes, with hundreds ofworked examples and probability and Fourier transform tables



This survival guide in probability and random processes eliminatesthe need to pore through several resources to find a certainformula or table. It offers a compendium of most distributionfunctions used by communication engineers, queuing theoryspecialists, signal processing engineers, biomedical engineers,physicists, and students.

Key topics covered include:
* Random variables and most of their frequently used discrete andcontinuous probability distribution functions
* Moments, transformations, and convergences of randomvariables
* Characteristic, generating, and moment-generating functions
* Computer generation of random variates
* Estimation theory and the associated orthogonalityprinciple
* Linear vector spaces and matrix theory with vector and matrixdifferentiation concepts
* Vector random variables
* Random processes and stationarity concepts
* Extensive classification of random processes
* Random processes through linear systems and the associated Wienerand Kalman filters
* Application of probability in single photon emission tomography(SPECT)


More than 400 figures drawn to scale assist readers inunderstanding and applying theory. Many of these figures accompanythe more than 300 examples given to help readers visualize how tosolve the problem at hand. In many instances, worked examples aresolved with more than one approach to illustrate how differentprobability methodologies can work for the same problem.

Several probability tables with accuracy up to nine decimal placesare provided in the appendices for quick reference. A specialfeature is the graphical presentation of the commonly occurringFourier transforms, where both time and frequency functions aredrawn to scale.

This book is of particular value to undergraduate and graduatestudents in electrical, computer, and civil engineering, as well asstudents in physics and applied mathematics. Engineers, computerscientists, biostatisticians, and researchers in communicationswill also benefit from having a single resource to address mostissues in probability and random processes.

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Contents

CHAPTER 1 Sets Fields and Events
1
CHAPTER 2 Probability Space and Axioms
10
CHAPTER 3 Basic Combinatorics
25
CHAPTER 4 Discrete Distributions
37
CHAPTER 5 Random Variables
64
CHAPTER 6 Continuous Random Variables and Basic Distributions
79
CHAPTER 7 Other Continuous Distributions
95
CHAPTER 8 Conditional Densities and Distributions
122
CHAPTER 15 Computer Methods for Generating Random Variates
264
CHAPTER 16 Elements of Matrix Algebra
284
CHAPTER 17 Random Vectors and MeanSquare Estimation
311
CHAPTER 18 Estimation Theory
340
CHAPTER 19 Random Processes
406
CHAPTER 20 Classification of Random Processes
490
CHAPTER 21 Random Processes and Linear Systems
574
CHAPTER 22 Weiner and Kalman Filters
625

CHAPTER 9 Joint Densities and Distributions
135
CHAPTER 10 Moments and Conditional Moments
146
CHAPTER 11 Characteristic Functions and Generating Functions
155
CHAPTER 12 Functions of a Single Random Variable
173
CHAPTER 13 Functions of Multiple Random Variables
206
CHAPTER 14 Inequalities Convergences and Limit Theorems
241
CHAPTER 23 Probabilistic Methods in Transmission Tomography
666
APPENDIXES
683
References
714
Index
716
Copyright

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Page 543 - A system is non-decomposable if every state can be reached from every other state in a finite number of steps, that is, there exists an integer n > 1 such that Pij(n) > 0.
Page 7 - AU (BUC) = (AUB) UC, A n (B n C) = (A n B) n c.
Page 287 - Similarly, the row rank of a matrix is the number of linearly independent rows. If...
Page 154 - Using (2.12) and (2.13), the result that the absolute value of an integral is less than or equal to the integral of the...
Page 293 - The n roots of the characteristic equation are called the eigenvalues of the matrix A, and in linear systems they are also known as the "poles
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Page 140 - The joint probability density function of two random variables x and y...
Page 258 - ... 5.5 Let {Xn} be a sequence of independent identically distributed random variables with means 0 and variances 1. Let Sn = Xi + Xz + • • • + Xn be the sequence of their consecutive sums. For n= 1, 2, • • • define a stochastic process {Yn(t), 0 < t < 1} as follows...
Page 283 - The first subscript denotes the row, and the second subscript denotes the column.
Page 5 - Finally, the difference of two sets A and B, denoted by A — B, is the set of all elements of A that are not elements of B. A — B = {x: xe A and x $ B} For example, {1,3, 9} -{3, 5, 7} = {1,9}.

About the author (2006)

VENKATARAMA KRISHNAN, PhD, is Professor Emeritus in the Department of Electrical Engineering at the University of Massachusetts Lowell. Previously, he has taught at the Indian Institute of Science, Polytechnic University, the University of Pennsylvania, Princeton University, Villanova University, and Smith College. He also worked for two years (1974–1976) as a senior systems analyst for Dynamics Research Corporation on estimation problems associated with navigation and guidance and continued as their consultant for more than a decade. Professor Krishnan's research interests include estimation of steady-state queue distributions, tomographic imaging, biosystems, and digital, aerospace, control, communications, and stochastic systems. As a senior member of IEEE, Dr. Krishnan has authored three other books in addition to technical publications.

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