Roy Yates received the B.S.E. degree in 1983 from Princeton and the S.M. and Ph.D. degrees in 1986 and 1990 from MIT, all in Electrical Engineering. Since 1990, he has been with the Wireless Information Networks Laboratory (WINLAB) and the ECE department at Rutgers University. Presently, he is an Associate Director of WINLAB and a Professor in the ECE Dept. He is a co-author (with David Goodman) of the text Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers published by John Wiley and Sons. He is a co-recipient (with Christopher Rose and Sennur Ulukus) of the 2003 IEEE Marconi Prize Paper Award in Wireless Communications. His research interests include power control, interference suppression and spectrum regulation for wireless systems.

• Features of this Text i Preface vii1 Experiments, Models, and Probabilities 1Getting Started with Probability 11.1 Set Theory 31.2 Applying Set Theory to Probability 71.3 Probability Axioms 111.4 Conditional Probability 151.5 Partitions and the Law of Total Probability 181.6 Independence 241.7 Matlab 27Problems 292 Sequential Experiments 352.1 Tree Diagrams 352.2 Counting Methods 402.3 Independent Trials 492.4 Reliability Analysis 522.5 Matlab 55Problems 573 Discrete Random Variables 623.1 Definitions 623.2 Probability Mass Function 653.3 Families of Discrete Random Variables 683.4 Cumulative Distribution Function (CDF) 773.5 Averages and Expected Value 803.6 Functions of a Random Variable 863.7 Expected Value of a Derived Random Variable 903.8 Variance and Standard Deviation 933.9 Matlab 99Problems 1064 Continuous Random Variables 1184.1 Continuous Sample Space 1184.2 The Cumulative Distribution Function 1214.3 Probability Density Function 1234.4 Expected Values 1284.5 Families of Continuous Random Variables 1324.6 Gaussian Random Variables 1384.7 Delta Functions, Mixed Random Variables 1454.8 Matlab 152Problems 1545 Multiple Random Variables 1625.1 Joint Cumulative Distribution Function 1635.2 Joint Probability Mass Function 1665.3 Marginal PMF 1695.4 Joint Probability Density Function 1715.5 Marginal PDF 1775.6 Independent Random Variables 1785.7 Expected Value of a Function of Two Random Variables 1815.8 Covariance, Correlation and Independence 1845.9 Bivariate Gaussian Random Variables 1915.10 Multivariate Probability Models 1955.11 Matlab 201Problems 2066 Probability Models of Derived Random Variables 2186.1 PMF of a Function of Two Discrete Random Variables 2196.2 Functions Yielding Continuous Random Variables 2206.3 Functions Yielding Discrete or Mixed Random Variables 2266.4 Continuous Functions of Two Continuous Random Variables 2296.5 PDF of the Sum of Two Random Variables 2326.6 Matlab 234Problems 2367 Conditional Probability Models 2427.1 Conditioning a Random Variable by an Event 2427.2 Conditional Expected Value Given an Event 2487.3 Conditioning Two Random Variables by an Event 2527.4 Conditioning by a Random Variable 2567.5 Conditional Expected Value Given a Random Variable 2627.6 Bivariate Gaussian Random Variables: Conditional PDFs 2657.7 Matlab 268Problems 2698 Random Vectors 2778.1 Vector Notation 2778.2 Independent Random Variables and Random Vectors 2808.3 Functions of Random Vectors 2818.4 Expected Value Vector and Correlation Matrix 2858.5 Gaussian Random Vectors 2918.6 Matlab 298Problems 3009 Sums of Random Variables 3069.1 Expected Values of Sums 3069.2 Moment Generating Functions 3109.3 MGF of the Sum of Independent Random Variables 3149.4 Random Sums of Independent Random Variables 3179.5 Central Limit Theorem 3219.6 Matlab 328Problems 33110 The Sample Mean 33710.1 Sample Mean: Expected Value and Variance 33710.2 Deviation of a Random Variable from the Expected Value 33910.3 Laws of Large Numbers 34310.4 Point Estimates of Model Parameters 34510.5 Confidence Intervals 35210.6 Matlab 358Problems 36011 Hypothesis Testing 36611.1 Significance Testing 36711.2 Binary Hypothesis Testing 37011.3 Multiple Hypothesis Test 38411.4 Matlab 387Problems 38912 Estimation of a Random Variable 39912.1 Minimum Mean Square Error Estimation 40012.2 Linear Estimation of X given Y 40412.3 MAP and ML Estimation 40912.4 Linear Estimation of Random Variables from Random Vectors 41412.5 Matlab 421Problems 42313 Stochastic Processes 42913.1 Definitions and Examples 43013.2 Random Variables from Random Processes 43513.3 Independent, Identically Distributed Random Sequences 43713.4 The Poisson Process 43913.5 Properties of the Poisson Process 44313.6 The Brownian Motion Process 44613.7 Expected Value and Correlation 44813.8 Stationary Processes 45213.9 Wide Sense Stationary Stochastic Processes 45513.10 Cross-Correlation 45913.11 Gaussian Processes 46213.12 Matlab 464Problems 468Appendix A Families of Random Variables 477A.1 Discrete Random Variables 477A.2 Continuous Random Variables 479Appendix B A Few Math Facts 483References 489Index 491