Mathematical statistics. (Q2735594)

This book is a collection of problems and exercises on mathematical statistics with description of basic notions and main principles. It provides a solid introduction to statistics for students in a one-semester course. The contents of the book are as follows:NEWLINENEWLINENEWLINE1. Estimation of parameters of distributions: point estimates; efficient estimates; the Rao-Cramér inequality. 2. Methods of construction of estimates: empirical estimates; method of moments; maximum-likelihood method. 3. Hypothesis testing: criteria; power of criteria. 4. Hypothesis tests for parameters of the normal distribution. 5. Chi-square tests: chi-square goodness-of-fit test; chi-square independence test. 6. Nonparametric criteria: Kolmogorov-Smirnov test; Wilcoxon signed-rank test. All necessary tables (normal distribution, \(\chi^2\)-distribution, Student distribution, Kolmogorov distribution, Fisher distribution, binomial distribution, Poisson distribution, etc.) are presented.NEWLINENEWLINENEWLINEWith a minimum of mathematical theory, the author has covered the binomial, Poisson and normal distributions; hypothesis testing, nonparametric hypothesis tests, and chi-square goodness-of-fit tests in an easy to understand style. This book is useful to all those who want to learn statistics. Each chapter has a number of problems. By solving these problems students understand and appreciate the subject.