{"product_id":"probability-and-stochastic-processes-isbn-9781118324561","title":"Probability and Stochastic Processes","description":"\u003cp\u003eThis text introduces engineering students to probability theory and stochastic processes. Along with thorough mathematical development of the subject, the book presents intuitive explanations of key points in order to give students the insights they need to apply math to practical engineering problems. The first five chapters contain the core material that is essential to any introductory course. In one-semester undergraduate courses, instructors can select material from the remaining chapters to meet their individual goals. Graduate courses can cover all chapters in one semester. \u003c\/p\u003e Features of this Text i \u003cp\u003ePreface vii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Experiments, Models, and Probabilities 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eGetting Started with Probability 1\u003c\/p\u003e \u003cp\u003e1.1 Set Theory 3\u003c\/p\u003e \u003cp\u003e1.2 Applying Set Theory to Probability 7\u003c\/p\u003e \u003cp\u003e1.3 Probability Axioms 11\u003c\/p\u003e \u003cp\u003e1.4 Conditional Probability 15\u003c\/p\u003e \u003cp\u003e1.5 Partitions and the Law of Total Probability 18\u003c\/p\u003e \u003cp\u003e1.6 Independence 24\u003c\/p\u003e \u003cp\u003e1.7 Matlab 27\u003c\/p\u003e \u003cp\u003eProblems 29\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Sequential Experiments 35\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Tree Diagrams 35\u003c\/p\u003e \u003cp\u003e2.2 Counting Methods 40\u003c\/p\u003e \u003cp\u003e2.3 Independent Trials 49\u003c\/p\u003e \u003cp\u003e2.4 Reliability Analysis 52\u003c\/p\u003e \u003cp\u003e2.5 Matlab 55\u003c\/p\u003e \u003cp\u003eProblems 57\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Discrete Random Variables 62\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Definitions 62\u003c\/p\u003e \u003cp\u003e3.2 Probability Mass Function 65\u003c\/p\u003e \u003cp\u003e3.3 Families of Discrete Random Variables 68\u003c\/p\u003e \u003cp\u003e3.4 Cumulative Distribution Function (CDF) 77\u003c\/p\u003e \u003cp\u003e3.5 Averages and Expected Value 80\u003c\/p\u003e \u003cp\u003e3.6 Functions of a Random Variable 86\u003c\/p\u003e \u003cp\u003e3.7 Expected Value of a Derived Random Variable 90\u003c\/p\u003e \u003cp\u003e3.8 Variance and Standard Deviation 93\u003c\/p\u003e \u003cp\u003e3.9 Matlab 99\u003c\/p\u003e \u003cp\u003eProblems 106\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Continuous Random Variables 118\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Continuous Sample Space 118\u003c\/p\u003e \u003cp\u003e4.2 The Cumulative Distribution Function 121\u003c\/p\u003e \u003cp\u003e4.3 Probability Density Function 123\u003c\/p\u003e \u003cp\u003e4.4 Expected Values 128\u003c\/p\u003e \u003cp\u003e4.5 Families of Continuous Random Variables 132\u003c\/p\u003e \u003cp\u003e4.6 Gaussian Random Variables 138\u003c\/p\u003e \u003cp\u003e4.7 Delta Functions, Mixed Random Variables 145\u003c\/p\u003e \u003cp\u003e4.8 Matlab 152\u003c\/p\u003e \u003cp\u003eProblems 154\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Multiple Random Variables 162\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Joint Cumulative Distribution Function 163\u003c\/p\u003e \u003cp\u003e5.2 Joint Probability Mass Function 166\u003c\/p\u003e \u003cp\u003e5.3 Marginal PMF 169\u003c\/p\u003e \u003cp\u003e5.4 Joint Probability Density Function 171\u003c\/p\u003e \u003cp\u003e5.5 Marginal PDF 177\u003c\/p\u003e \u003cp\u003e5.6 Independent Random Variables 178\u003c\/p\u003e \u003cp\u003e5.7 Expected Value of a Function of Two Random Variables 181\u003c\/p\u003e \u003cp\u003e5.8 Covariance, Correlation and Independence 184\u003c\/p\u003e \u003cp\u003e5.9 Bivariate Gaussian Random Variables 191\u003c\/p\u003e \u003cp\u003e5.10 Multivariate Probability Models 195\u003c\/p\u003e \u003cp\u003e5.11 Matlab 201\u003c\/p\u003e \u003cp\u003eProblems 206\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Probability Models of Derived Random Variables 218\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 PMF of a Function of Two Discrete Random Variables 219\u003c\/p\u003e \u003cp\u003e6.2 Functions Yielding Continuous Random Variables 220\u003c\/p\u003e \u003cp\u003e6.3 Functions Yielding Discrete or Mixed Random Variables 226\u003c\/p\u003e \u003cp\u003e6.4 Continuous Functions of Two Continuous Random Variables 229\u003c\/p\u003e \u003cp\u003e6.5 PDF of the Sum of Two Random Variables 232\u003c\/p\u003e \u003cp\u003e6.6 Matlab 234\u003c\/p\u003e \u003cp\u003eProblems 236\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Conditional Probability Models 242\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Conditioning a Random Variable by an Event 242\u003c\/p\u003e \u003cp\u003e7.2 Conditional Expected Value Given an Event 248\u003c\/p\u003e \u003cp\u003e7.3 Conditioning Two Random Variables by an Event 252\u003c\/p\u003e \u003cp\u003e7.4 Conditioning by a Random Variable 256\u003c\/p\u003e \u003cp\u003e7.5 Conditional Expected Value Given a Random Variable 262\u003c\/p\u003e \u003cp\u003e7.6 Bivariate Gaussian Random Variables: Conditional PDFs 265\u003c\/p\u003e \u003cp\u003e7.7 Matlab 268\u003c\/p\u003e \u003cp\u003eProblems 269\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 Random Vectors 277\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Vector Notation 277\u003c\/p\u003e \u003cp\u003e8.2 Independent Random Variables and Random Vectors 280\u003c\/p\u003e \u003cp\u003e8.3 Functions of Random Vectors 281\u003c\/p\u003e \u003cp\u003e8.4 Expected Value Vector and Correlation Matrix 285\u003c\/p\u003e \u003cp\u003e8.5 Gaussian Random Vectors 291\u003c\/p\u003e \u003cp\u003e8.6 Matlab 298\u003c\/p\u003e \u003cp\u003eProblems 300\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Sums of Random Variables 306\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Expected Values of Sums 306\u003c\/p\u003e \u003cp\u003e9.2 Moment Generating Functions 310\u003c\/p\u003e \u003cp\u003e9.3 MGF of the Sum of Independent Random Variables 314\u003c\/p\u003e \u003cp\u003e9.4 Random Sums of Independent Random Variables 317\u003c\/p\u003e \u003cp\u003e9.5 Central Limit Theorem 321\u003c\/p\u003e \u003cp\u003e9.6 Matlab 328\u003c\/p\u003e \u003cp\u003eProblems 331\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 The Sample Mean 337\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Sample Mean: Expected Value and Variance 337\u003c\/p\u003e \u003cp\u003e10.2 Deviation of a Random Variable from the Expected Value 339\u003c\/p\u003e \u003cp\u003e10.3 Laws of Large Numbers 343\u003c\/p\u003e \u003cp\u003e10.4 Point Estimates of Model Parameters 345\u003c\/p\u003e \u003cp\u003e10.5 Confidence Intervals 352\u003c\/p\u003e \u003cp\u003e10.6 Matlab 358\u003c\/p\u003e \u003cp\u003eProblems 360\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Hypothesis Testing 366\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Significance Testing 367\u003c\/p\u003e \u003cp\u003e11.2 Binary Hypothesis Testing 370\u003c\/p\u003e \u003cp\u003e11.3 Multiple Hypothesis Test 384\u003c\/p\u003e \u003cp\u003e11.4 Matlab 387\u003c\/p\u003e \u003cp\u003eProblems 389\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 Estimation of a Random Variable 399\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 Minimum Mean Square Error Estimation 400\u003c\/p\u003e \u003cp\u003e12.2 Linear Estimation of X given Y 404\u003c\/p\u003e \u003cp\u003e12.3 MAP and ML Estimation 409\u003c\/p\u003e \u003cp\u003e12.4 Linear Estimation of Random Variables from Random Vectors 414\u003c\/p\u003e \u003cp\u003e12.5 Matlab 421\u003c\/p\u003e \u003cp\u003eProblems 423\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 Stochastic Processes 429\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 Definitions and Examples 430\u003c\/p\u003e \u003cp\u003e13.2 Random Variables from Random Processes 435\u003c\/p\u003e \u003cp\u003e13.3 Independent, Identically Distributed Random Sequences 437\u003c\/p\u003e \u003cp\u003e13.4 The Poisson Process 439\u003c\/p\u003e \u003cp\u003e13.5 Properties of the Poisson Process 443\u003c\/p\u003e \u003cp\u003e13.6 The Brownian Motion Process 446\u003c\/p\u003e \u003cp\u003e13.7 Expected Value and Correlation 448\u003c\/p\u003e \u003cp\u003e13.8 Stationary Processes 452\u003c\/p\u003e \u003cp\u003e13.9 Wide Sense Stationary Stochastic Processes 455\u003c\/p\u003e \u003cp\u003e13.10 Cross-Correlation 459\u003c\/p\u003e \u003cp\u003e13.11 Gaussian Processes 462\u003c\/p\u003e \u003cp\u003e13.12 Matlab 464\u003c\/p\u003e \u003cp\u003eProblems 468\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix A Families of Random Variables 477\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eA.1 Discrete Random Variables 477\u003c\/p\u003e \u003cp\u003eA.2 Continuous Random Variables 479\u003c\/p\u003e \u003cp\u003e\u003cb\u003eAppendix B A Few Math Facts 483\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003eReferences 489\u003c\/p\u003e \u003cp\u003eIndex 491\u003c\/p\u003e \u003cp\u003e\u003cb\u003eRoy Yates\u003c\/b\u003e 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 \u003cb\u003eDavid Goodman\u003c\/b\u003e) of the text \u003ci\u003eProbability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers\u003c\/i\u003e 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.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989857747173,"sku":"NP9781118324561","price":162.0,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781118324561.jpg?v=1761785697","url":"https:\/\/k12savings.com\/es\/products\/probability-and-stochastic-processes-isbn-9781118324561","provider":"K12savings","version":"1.0","type":"link"}