This book is designed for use to meet the requirements of the students of Mathematical Statistics at Degree, Honours and Post Graduate levels. It provides comprehensive and exhaustive theoretical discussion. All basic concepts have been explained in an easy and understandable manner with simple illustration. So much Text book has been an essential part of the mathematical background which are use in mathematicians, engineering and other scientists. It gives the importance and wide applications of the subject matter. It aims to present an introduction to mathematical Statistics which will be found helpful to all readers regardless of their field of specialization. Here in this book gives fundamental discussion starting from the very introduction of that chapter with simple basic definations and theorem. All the basic definitions and theorem gives are simple and easy language with appropriate examples in a systematic way. More material has been included than can be covered in most first courses. This has been done to make the book more feasible, to provide a useful book of reference and to stimulate further interest in the subject. Although there is a large number of books available covering various aspect in the field of mathematical statistics, there is no comprehensive book dealing with the various topics on mathematical statistics for the students. The present book is a modest though determined bid to meet the requirement of the students of mathematical Statistics but also carry the student on to such a level can read with profit the numerous special monographs which are available in the subject. In any branch of mathematics, it is certainly the teacher who holds the key to successful learning. The aim of this book has been simply to assist the teacher in conveying to the students more effectively a thorough understanding of mathematical statistics.