# Introduction to Mathematical Statistics

introduction to Mathematical Statistics is a comprehensive book for undergraduate students of Physics and Mathematics. The book comprises chapters on probability and distributions, multivariate distributions, maximum likelihood methods, and is a comprehensive book for undergraduate students of Physics and Mathematics. The book comprises chapters on probability and distributions, multivariate distributions, maximum likelihood methods, and Bayesian statistics. In addition, the book consists of chapter-wise questions and practice exercises to help understand the concepts better. This book is essential for students of math preparing for competitive examinations like IIT-JAM and NET.

this seventh edition, our goal has remained steadfast: to produce an outstanding text in mathematical statistics. In this new edition, we have added examples and exercises to help clarify the exposition. For the same reason, we have moved some material forward. For example, we moved the discussion on some properties of linear combinations of random variables from Chapter 4 to Chapter 2. This helps in the discussion of statistical properties in Chapter 3 as well as in the new Chapter 4.

One of the major changes was moving the chapter on “Some Elementary Statistical Inferences,” from Chapter 5 to Chapter 4. This chapter on inference covers conﬁdence intervals and statistical tests of hypotheses, two of the most important concepts in statistical inference. We begin Chapter 4 with a discussion of a random sample and point estimation. We introduce point estimation via a brief discussion of maximum likelihood estimation (the theory of maximum likelihood inference is still fullly discussed in Chapter 6).

In Chapter 4, though, the discussion is illustrated with examples. After discussing point estimation in Chapter 4, we proceed onto conﬁdence intervals and hypotheses testing. Inference for the basic one- and two-sample problems (large and small samples) is presented. We illustrate this discussion with plenty of examples, several of which are concerned with real data. We have also added exercises dealing with real data. The discussion has also been updated; for example, exact conﬁdence intervals for the parameters of discrete distributions and bootstrap conﬁdence intervals and tests of hypotheses are discussed, both of which are being used more and more in practice. These changes enable a one-semester course to cover basic statistical theory with applications. Such a course would cover Chapters 1–4 and, depending on time, parts of Chapter 5. For two-semester courses, this basic understanding of statistical inference will prove quite helpful to students in the later chapters (6–8) on the statistical theory of inference. 