A rigorous, yet accessible, textbook for computer science students learning probability. It covers topics of interest to computer scientists, including randomized algorithms, simulation, statistical inference, and stochastic systems modeling. Replete with engaging real-world examples, exercises, and full-color illustrations.
A rigorous, yet accessible, textbook for computer science students learning probability. It covers topics of interest to computer scientists, including randomized algorithms, simulation, statistical inference, and stochastic systems modeling. Replete with engaging real-world examples, exercises, and full-color illustrations.
Mor Harchol-Balter is the Bruce J. Nelson Professor of Computer Science at Carnegie Mellon University. She is a Fellow of both ACM and IEEE. She has received numerous teaching awards, including the Herbert A. Simon Award for teaching excellence at CMU. She is also the author of the popular textbook Performance Analysis and Design of Computer Systems (Cambridge, 2013).
Inhaltsangabe
Preface Part I. Fundamentals and Probability on Events: 1. Before we start ... some mathematical basics 2. Probability on events Part II. Discrete Random Variables: 3. Probability and discrete random variables 4. Expectations 5. Variance, higher moments, and random sums 6. z-Transforms Part III. Continuous Random Variables: 7. Continuous random variables: single distribution 8. Continuous random variables: joint distributions 9. Normal distribution 10. Heavy tails: the distributions of computing 11. Laplace transforms Part IV. Computer Systems Modeling and Simulation: 12. The Poisson process 13. Generating random variables for simulation 14. Event-driven simulation Part V. Statistical Inference 15. Estimators for mean and variance 16. Classical statistical inference 17. Bayesian statistical inference Part VI. Tail Bounds and Applications: 18. Tail bounds 19. Applications of tail bounds: confidence intervals and balls-and-bins 20. Hashing algorithms Part VII. Randomized Algorithms: 21. Las Vegas randomized algorithms 22. Monte Carlo randomized algorithms 23. Primality testing Part VIII. Discrete-time Markov Chains 24. Discrete-time Markov chains: finite-state 25. Ergodicity for finite-state discrete-time Markov chains 26. Discrete-time Markov chains: infinite-state 27. A little bit of queueing theory References Index.
Preface Part I. Fundamentals and Probability on Events: 1. Before we start ... some mathematical basics 2. Probability on events Part II. Discrete Random Variables: 3. Probability and discrete random variables 4. Expectations 5. Variance, higher moments, and random sums 6. z-Transforms Part III. Continuous Random Variables: 7. Continuous random variables: single distribution 8. Continuous random variables: joint distributions 9. Normal distribution 10. Heavy tails: the distributions of computing 11. Laplace transforms Part IV. Computer Systems Modeling and Simulation: 12. The Poisson process 13. Generating random variables for simulation 14. Event-driven simulation Part V. Statistical Inference 15. Estimators for mean and variance 16. Classical statistical inference 17. Bayesian statistical inference Part VI. Tail Bounds and Applications: 18. Tail bounds 19. Applications of tail bounds: confidence intervals and balls-and-bins 20. Hashing algorithms Part VII. Randomized Algorithms: 21. Las Vegas randomized algorithms 22. Monte Carlo randomized algorithms 23. Primality testing Part VIII. Discrete-time Markov Chains 24. Discrete-time Markov chains: finite-state 25. Ergodicity for finite-state discrete-time Markov chains 26. Discrete-time Markov chains: infinite-state 27. A little bit of queueing theory References Index.
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