Probability theory 2. From standard deviation to statistical inference (Q2189834)

This monograph presents on a total of 421 pages an introduction into the basic concepts of probability theory and is organized in 12 chapters. It is the second volume of a series and addresses mainly to first-year students in courses with some basic mathematical knowledge. \par After a preface in Chapter 1, Chapter 2 concentrates on the concept of standard deviation including a general introduction as well as the application to Bernoulli processes and independent experiments. In Chapter 3 the use of the expected value and the standard deviation in the cost estimate for search processes in a data base is described. The following two chapters introduce main concepts of the probability theory: Chebyshev's inequality in Chapter 4 and the law of large numbers in Chapter 5. Chapter 6 deals with continuous random variables (univariate distribution, exponential decay, standardized normal distribution and Kolmogorov axioms). One of the most important distribution functions, the normal distributions, is presented and discussed in Chapter 7 before the central limit theorem is introduced in Chapter 8. The book ends with four chapters on applications. Chapter 9 deals with modelling of surveys. The concept of hypothesis testing is introduced in Chapter 10. Exemplary the Monte Carlo method as approximation approach as well as the Brownian motion are described in Chapter 11. The last Chapter 12 introduces the linear regression model. \par In summary, the book under review is strongly recommended to interested students. Each chapter of the book is enriched with a large number of examples and a huge set of supportive exercises and control questions supporting self-learning activities.