Introduction to Statistical Mathematics

de A. M. Mathai

This is an introductory book on Mathematics of stochastic variables. The book deals with elementary Probability and Statistics. This can be used as a book for self study or for a one year slow course in Probability and Statistics. Since it is also intended as a book for self study, the various symbols and letters used, are explained then and there throughout the book. The pre-requisite is one year Calculus. But a person with high school Mathematics can follow the book except the few sections which use Calculus extensively. In Chapter 1 an introduction to Set Theory and Linear Algebra is given. The pre. requisite for this chapter is only high school Mathematics. The later sections of Linear Algebra may be omitted because they are not very much used. These facts are mentioned in the different section s. An attempt is made to make the book semi-rigorous. It is a fairly balanced treatment of theory and applications and this will give a sufficiently good background for further studies. The book is based on the topics covered in an introductory course in Statistics for the General Arts and Science students at McGill University. The book is intended for : (1) self study. (2) a two semester course in Probability and Statistics. (3) a one semester course in Probability (Chapters 2.5). (4) a one year course in Indian universities. Special features : 1. A new approach—built up on stochastic variables and the operator called 'Mathematical Expectation' uniformity in notations. 2. Student's difficulty of distinguishing discrete, continuous, finite, infinite, observed and hypothetical populations, is avoided by properly defining and developing the theory, based on the theory of sets. 3. The dialogue is designed to suit the particular age group of students who are likely to take the course. 4. A number of worked examples are given in each section and a good number of examples are taken from problems of day to day life. 5. The development of the theory is very slow in the be. ginning chapters and the discussion is precise and a minimum in later chapters. 6. An insight into the advanced and various related topics, is given to the reader in every section. 7. Summary of correspondence between topics, important results, formulae etc. is given in every chapter.