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[null,"1.","Record Nr.",null,"UNINA9910488709003321"]
[null,null,"Autore",null,"Walrand Jean"]
[null,null,"Titolo",null,"Probability in Electrical Engineering and Computer Science : An Application-Driven Course"]
[null,null,"Pubbl/distr/stampa",null,"Cham, : Springer International Publishing AG, 2021"]
[null,null,"ISBN",null,"3-030-49995-2"]
[null,null,"Edizione",null,"[1st ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource (390 p.)"]
[null,null,"Soggetti",null,"Maths for computer scientists"]
[{"$nulls":4},"Communications engineering / telecommunications"]
[{"$nulls":4},"Maths for engineers"]
[{"$nulls":4},"Probability & statistics"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,"Nota di contenuto",null,"Intro -- Preface -- Acknowledgements -- Introduction -- About This Second Edition -- Contents -- 1 PageRank: A -- 1.1 Model -- 1.2 Markov Chain -- 1.2.1 General Definition -- 1.2.2 Distribution After n Steps and Invariant Distribution -- 1.3 Analysis -- 1.3.1 Irreducibility and Aperiodicity -- 1.3.2 Big Theorem -- 1.3.3 Long-Term Fraction of Time -- 1.4 Illustrations -- 1.5 Hitting Time -- 1.5.1 Mean Hitting Time -- 1.5.2 Probability of Hitting a State Before Another -- 1.5.3 FSE for Markov Chain -- 1.6 Summary -- 1.6.1 Key Equations and Formulas -- 1.7 References -- 1.8 Problems -- 2 PageRank: B -- 2.1 Sample Space -- 2.2 Laws of Large Numbers for Coin Flips -- 2.2.1 Convergence in Probability -- 2.2.2 Almost Sure Convergence -- 2.3 Laws of Large Numbers for i.i.d. RVs -- 2.3.1 Weak Law of Large Numbers -- 2.3.2 Strong Law of Large Numbers -- 2.4 Law of Large Numbers for Markov Chains -- 2.5 Proof of Big Theorem -- 2.5.1 Proof of Theorem 1.1 (a) -- 2.5.2 Proof of Theorem 1.1 (b) -- 2.5.3 Periodicity -- 2.6 Summary -- 2.6.1 Key Equations and Formulas -- 2.7 References -- 2.8 Problems -- 3 Multiplexing: A -- 3.1 Sharing Links -- 3.2 Gaussian Random Variable and CLT -- 3.2.1 Binomial and Gaussian -- 3.2.2 Multiplexing and Gaussian -- 3.2.3 Confidence Intervals -- 3.3 Buffers -- 3.3.1 Markov Chain Model of Buffer -- 3.3.2 Invariant Distribution -- 3.3.3 Average Delay -- 3.3.4 A Note About Arrivals -- 3.3.5 Little's Law -- 3.4 Multiple Access -- 3.5 Summary -- 3.5.1 Key Equations and Formulas -- 3.6 References -- 3.7 Problems "]
[{"$nulls":4},"-- 4 Multiplexing: B -- 4.1 Characteristic Functions -- 4.2 Proof of CLT (Sketch) -- 4.3 Moments of N(0, 1) -- 4.4 Sum of Squares of 2 i.i.d. N(0, 1) -- 4.5 Two Applications of Characteristic Functions -- 4.5.1 Poisson as a Limit of Binomial -- 4.5.2 Exponential as Limit of Geometric -- 4.6 Error Function."]
[{"$nulls":4},"4.7 Adaptive Multiple Access -- 4.8 Summary -- 4.8.1 Key Equations and Formulas -- 4.9 References -- 4.10 Problems -- 5 Networks: A -- 5.1 Spreading Rumors -- 5.2 Cascades -- 5.3 Seeding the Market -- 5.4 Manufacturing of Consent -- 5.5 Polarization -- 5.6 M/M/1 Queue -- 5.7 Network of Queues -- 5.8 Optimizing Capacity -- 5.9 Internet and Network of Queues -- 5.10 Product-Form Networks -- 5.10.1 Example -- 5.11 References -- 5.12 Problems -- 6 Networks-B -- 6.1 Social Networks -- 6.2 Continuous-Time Markov Chains -- 6.2.1 Two-State Markov Chain -- 6.2.2 Three-State Markov Chain -- 6.2.3 General Case -- 6.2.4 Uniformization -- 6.2.5 Time Reversal -- 6.3 Product-Form Networks -- 6.4 Proof of Theorem 5.7 -- 6.5 References -- 7 Digital Link-A -- 7.1 Digital Link -- 7.2 Detection and Bayes' Rule -- 7.2.1 Bayes' Rule -- 7.2.2 Circumstances vs. Causes -- 7.2.3 MAP and MLE -- Example: Ice Cream and Sunburn -- 7.2.4 Binary Symmetric Channel -- 7.3 Huffman Codes -- 7.4 Gaussian Channel -- Simulation -- 7.4.1 BPSK -- 7.5 Multidimensional Gaussian Channel -- 7.5.1 MLE in Multidimensional Case -- 7.6 Hypothesis Testing -- 7.6.1 Formulation -- 7.6.2 Solution -- 7.6.3 Examples -- Gaussian Channel -- Mean of Exponential RVs -- Bias of a Coin -- Discrete Observations -- 7.7 Summary -- 7.7.1 Key Equations and Formulas -- 7.8 References -- 7.9 Problems -- 8 Digital Link-B -- 8.1 Proof of Optimality of the Huffman Code -- 8.2 Proof of Neyman-Pearson Theorem 7.4 -- 8.3 Jointly Gaussian Random Variables -- 8.3.1 Density of Jointly Gaussian Random Variables -- 8.4 Elementary Statistics -- 8.4.1 Zero-Mean? -- 8.4.2 Unknown Variance -- 8.4.3 Difference of Means -- 8.4.4 Mean in Hyperplane? -- 8.4.5 ANOVA -- 8.5 LDPC Codes -- 8.6 Summary -- 8.6.1 Key Equations and Formulas -- 8.7 References -- 8.8 Problems -- 9 Tracking-A -- 9.1 Examples -- 9.2 Estimation Problem."]
[{"$nulls":4},"9.3 Linear Least Squares Estimates -- 9.3.1 Projection -- 9.4 Linear Regression -- 9.5 A Note on Overfitting -- 9.6 MMSE -- 9.6.1 MMSE for Jointly Gaussian -- 9.7 Vector Case -- 9.8 Kalman Filter -- 9.8.1 The Filter -- 9.8.2 Examples -- Random Walk -- Random Walk with Unknown Drift -- Random Walk with Changing Drift -- Falling Object -- 9.9 Summary -- 9.9.1 Key Equations and Formulas -- 9.10 References -- 9.11 Problems -- 10 Tracking: B -- 10.1 Updating LLSE -- 10.2 Derivation of Kalman Filter -- 10.3 Properties of Kalman Filter -- 10.3.1 Observability -- 10.3.2 Reachability -- 10.4 Extended Kalman Filter -- 10.4.1 Examples -- 10.5 Summary -- 10.5.1 Key Equations and Formulas -- 10.6 References -- 11 Speech Recognition: A -- 11.1 Learning: Concepts and Examples -- 11.2 Hidden Markov Chain -- 11.3 Expectation Maximization and Clustering -- 11.3.1 A Simple Clustering Problem -- 11.3.2 A Second Look -- 11.4 Learning: Hidden Markov Chain -- 11.4.1 HEM -- 11.4.2 Training the Viterbi Algorithm -- 11.5 Summary -- 11.5.1 Key Equations and Formulas -- 11.6 References -- 11.7 Problems -- 12 Speech Recognition: B -- 12.1 Online Linear Regression -- 12.2 Theory of Stochastic Gradient Projection -- 12.2.1 Gradient Projection -- 12.2.2 Stochastic Gradient Projection -- 12.2.3 Martingale Convergence -- 12.3 Big Data -- 12.3.1 Relevant Data -- 12.3.2 Compressed Sensing -- 12.3.3 Recommendation Systems -- 12.4 Deep Neural Networks -- 12.4.1 Calculating Derivatives -- 12.5 Summary -- 12.5.1 Key Equations and Formulas -- 12.6 References -- 12.7 Problems -- 13 Route Planning: A "]
[{"$nulls":4},"-- 13.1 Model -- 13.2 Formulation 1: Pre-planning -- 13.3 Formulation 2: Adapting -- 13.4 Markov Decision Problem -- 13.4.1 Examples -- 13.5 Infinite Horizon -- 13.6 Summary -- 13.6.1 Key Equations and Formulas -- 13.7 References -- 13.8 Problems -- 14 Route Planning: B -- 14.1 LQG Control."]
[{"$nulls":4},"14.1.1 Letting N →∞ -- 14.2 LQG with Noisy Observations -- 14.2.1 Letting N →∞ -- 14.3 Partially Observed MDP -- 14.3.1 Example: Searching for Your Keys -- 14.4 Summary -- 14.4.1 Key Equations and Formulas -- 14.5 References -- 14.6 Problems -- 15 Perspective and Complements -- 15.1 Inference -- 15.2 Sufficient Statistic -- 15.2.1 Interpretation -- 15.3 Infinite Markov Chains -- 15.3.1 Lyapunov-Foster Criterion -- 15.4 Poisson Process -- 15.4.1 Definition -- 15.4.2 Independent Increments -- 15.4.3 Number of Jumps -- 15.5 Boosting -- 15.6 Multi-Armed Bandits -- 15.7 Capacity of BSC -- 15.8 Bounds on Probabilities -- 15.8.1 Applying the Bounds to Multiplexing -- 15.9 Martingales -- 15.9.1 Definitions -- 15.9.2 Examples -- 15.9.3  Law of Large Numbers -- 15.9.4 Wald's Equality -- 15.10 Summary -- 15.10.1 Key Equations and Formulas -- 15.11 References -- 15.12 Problems -- Correction to: Probability in Electrical Engineering and Computer Science -- Correction to: Probability in Electrical Engineering and Computer Science (Funding Information) -- A Elementary Probability -- A.1 Symmetry -- A.2 Conditioning -- A.3 Common Confusion -- A.4 Independence -- A.5 Expectation -- A.6 Variance -- A.7 Inequalities -- A.8 Law of Large Numbers -- A.9 Covariance and Regression -- A.10 Why Do We Need a More Sophisticated Formalism? -- A.11 References -- A.12 Solved Problems -- B Basic Probability -- B.1 General Framework -- B.1.1 Probability Space -- B.1.2 Borel-Cantelli Theorem -- B.1.3 Independence -- B.1.4 Converse of Borel-Cantelli Theorem -- B.1.5 Conditional Probability -- B.1.6 Random Variable -- B.2 Discrete Random Variable -- B.2.1 Definition -- B.2.2 Expectation -- B.2.3 Function of a RV -- B.2.4 Nonnegative RV -- B.2.5 Linearity of Expectation -- B.2.6 Monotonicity of Expectation -- B.2.7 Variance, Standard Deviation."]
[{"$nulls":4},"B.2.8 Important Discrete Random Variables -- B.3 Multiple Discrete Random Variables -- B.3.1 Joint Distribution -- B.3.2 Independence -- B.3.3 Expectation of Function of Multiple RVs -- B.3.4 Covariance -- B.3.5 Conditional Expectation -- B.3.6 Conditional Expectation of a Function -- B.4 General Random Variables -- B.4.1 Definitions -- B.4.2 Examples -- B.4.3 Expectation -- B.4.4 Continuity of Expectation -- B.5 Multiple Random Variables -- B.5.1 Random Vector -- B.5.2 Minimum and Maximum of Independent RVs -- B.5.3 Sum of Independent Random Variables -- B.6 Random Vectors -- B.6.1 Orthogonality and Projection -- B.7 Density of a Function of Random Variables -- B.7.1 Linear Transformations -- B.7.2 Nonlinear Transformations -- B.8 References -- B.9 Problems -- References -- Index."]
[null,null,null,"Sommario/riassunto","This revised textbook motivates and illustrates the techniques of applied probability by applications in electrical engineering and computer science (EECS). The author presents information processing and communication systems that use algorithms based on probabilistic models and techniques, including web searches, digital links, speech recognition, GPS, route planning, recommendation systems, classification, and estimation. He then explains how these applications work and, along the way, provides the readers with the understanding of the key concepts and methods of applied probability. Python labs enable the readers to experiment and consolidate their understanding. The book includes homework, solutions, and Jupyter notebooks. This edition includes new topics such as Boosting, Multi-armed bandits, "]
[{"$nulls":4},"statistical tests, social networks, queuing networks, and neural networks. For ancillaries related to this book, including examples of Python demos and also Python labs used in Berkeley, please email Mary James at mary.james@springer.com. This is an open access book."]