Problems in Mathematical Statistics | G. I. Ivchenko, Yu. I. Medvedev, A. V. Chistyakov

This problem book covers all the traditional topics in modern statistical theory and is designed for students at technical colleges and universities who have mathematical statistics as an obligatory course. The problems are mostly analytical. The student is asked to prove the validity or an assertion or carry out an investigation. This will help him grasp the main aspects of mathematical statistics. Some of the problems are more difficult and can be used as individual assignments for course papers. We have included problems on computer simulation of random variables in order to obtain the data for statistical interpretation. Any âtheoreticalâ problem which contains a statistical algorithm for data analysis can be used (with the appropriate (practically infinite) choice of the model parameters ) to formulate a âpracticalâ problem. At the first stage the original data should be simulated using either published tables of random numbers or special computer programs. Then, by interpreting these âexperimentalâ results according to the algorithm in question, the student can compare the theoretical hypothesis with the original parameters which are known as they were used when the sample was simulated. All the problems differ in complexity. More difficult problems are marked with an asterisk and may require a significant effort on the part of the reader. Problems that cannot be reduced to standard algorithms are answered in detail or hints are given. Each chapter contains the basic notions, assertions, and formulas from the respective theoretical section. The statistical tables at the end of the book will help the reader obtain numerical results. The list of distributions will help him choose problems on different aspects of the same model.