Weighing the odds. A course in probability and statistics (Q2743217)

Written in the author's lively style, this textbook is an introduction to probability theory and statistics for undergraduate students. The level of the book is kept elementary: measure theory is avoided, basics of linear algebra are recalled. In its essentials the book is comparable to the textbook of \textit{G.R. Grimmett} and \textit{D.R. Stirzaker}, Probability and random processes. 2nd ed. (1992; Zbl 0759.60001), but rather aiming at statistics.NEWLINENEWLINENEWLINEEmphasis is placed on sharpening the students' intuition. This is reflected by a variety of examples, exercises and the discussions of many applications. A wealth of concrete calculations are carried out, such as moments, confidence intervals and likelihood functions. Numerous results are accompanied by a thorough discussion of their relation to former ones and their relevance for the theory. Not every result is proved, again more importance is attached to building up the readers' intuition and way of thinking. C or WINBUG code is provided for computational examples and simulations. The author cites a lot of further reading in the text, not only textbooks, but also some articles. In addition, in the appendix he lists a commented ``small sample of the literature'' to the different topics of the book.NEWLINENEWLINENEWLINEThe first five chapters are devoted to basic probability: 1) Introduction; 2) Events and Probabilities; 3) Random Variables, Means and Variances; 4) Conditioning and Independence; 5) Generating Functions; and the Central Limit Theorem. Besides the subjects mentioned in the titles of the chapters, this part is complemented by some topics usually not contained in textbooks. For example, the author introduces the Simple Random Walk and develops the Random Walk on Groups. Moreover, simulation of iid sequences is considered and some applications in genetics are constituted.NEWLINENEWLINENEWLINEThe following three chapters deal with statistics: 6) Confidence intervals for one-parameter models; 7) Conditional pdfs and multi-parameter Bayesian statistics; 8) Linear models, ANOVA, etc. All these chapters present both, the frequentists' and Bayesian approaches, and the differences between them are considered -- sometimes in a philosophical sense. Chapter 6) starts from the frequentists' basics, such as likelihood function, sufficient statistics and moves on to the Fisher information and the Kullback-Leibler relative entropy. The Bayesian part is rounded off by the Gibbs sampler in chapter 7. In chapter 9, ``Some Further Probability'', the author introduces conditional expectations, martingales and the Poisson process. The material is illustrated by some applications to finance and Wald's sequential hypothesis test. NEWLINENEWLINENEWLINEThe last chapter 10, ``Quantum Probability and Quantum Computing'', gives the foundations of quantum probability and presents some algorithms in quantum computing. In the last part of the chapter, the ideas of spin and entanglement are explained.