Introduction to Probability for Computing

ISBN-13: 9781009309073 / Angielski / Twarda / 2023 / 555 str.

Pennsylvania) Harchol-Balte Mor (Carnegie Mellon University

Opis

A highly engaging and interactive undergraduate textbook specifically written for computer science courses.

Recenzje

'I know probability theory, and have taught it to undergrads and grads at MIT, UC Berkeley, and Carnegie Mellon University. Yet this book has taught me some wonderfully interesting important material that I did not know. Mor is a great thinker, lecturer, and writer. I would love to have learned from this book as a student - and to have taught from it as an instructor!' Manuel Blum, University of California, Berkeley, and Carnegie Mellon University

Spis treści

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.