Introduction to Probability for Computing

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.