# Probability and Random Processes

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

This survival guide in probability and random processes eliminates the need to pore through several resources to find a certain formula or table. It offers a compendium of most distribution functions used by communication engineers, queuing theory specialists, signal processing engineers, biomedical engineers, physicists, and students.

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

More than 400 figures drawn to scale assist readers in understanding and applying theory. Many of these figures accompany the more than 300 examples given to help readers visualize how to solve the problem at hand. In many instances, worked examples are solved with more than one approach to illustrate how different probability methodologies can work for the same problem.

Several probability tables with accuracy up to nine decimal places are provided in the appendices for quick reference. A special feature is the graphical presentation of the commonly occurring Fourier transforms, where both time and frequency functions are drawn to scale.

This book is of particular value to undergraduate and graduate students in electrical, computer, and civil engineering, as well as students in physics and applied mathematics. Engineers, computer scientists, biostatisticians, and researchers in communications will also benefit from having a single resource to address most issues 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

### Popular passages

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
Page 424 - V , it is necessary and sufficient that the following two conditions be satisfied: 1) EJ ^ 0 does not belong to the code V 2) E.
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}.