Stochastics for computer scientists (Q1869580)

This book grew out of lectures for a course in Stochastics (Probability and Statistics) I--III for computer science students in the fourth semester and beyond of university studies in the Medical University of Lübeck. It corresponds perhaps to a senior or first year graduate level stochastics course in the USA. The first eight chapters are on discrete probability spaces and random variables, but when general probability spaces are introduced in Chapter 9, \(\sigma\)-algebras and measures are introduced and used thereafter. Following are the chapter headings: 1. Introduction. 2. Laplace distributions and discrete models. 3. Conditional probability and stochastic independence. 4. Random variables and special distributions. 5. Statistical applications: confidence domains. 6. Expected value and standard deviation. 7. Generating functions and exponential inequalities. 8. Information theory. 9. General probability spaces. 10. Integrals and expected values. 11. Computer simulation of random variables. 12. Markov chains. 13. Approximation of distributions. 14. Maximum-likelihood estimators and the expectation-maximization algorithm. Appendix: An optimization method of Lagrange; Stirling's approximation formula. Each chapter has a good selection of exercises. No answers or solution sketches are given, but many call for proof of a given assertion. The now celebrated problem based on the American television show ``Let's make a deal'' occurs as Exercise 1 in Chapter 3.