Probability and Statistics

This book is an introduction to basic statistical concepts and their applications. The only prerequisite is some knowledge of differential and integral calculus, which can be picked up in fifteen one-hour lectures. All other mathematical requirements are given in the book itself, in the form of technical notes. The book is intended to give a clear picture of basic statistical concepts. Since the theory of sets is usually taught in secondary schools, only the concepts needed for a meaningful discussion of basic probability theory and statistical populations are discussed; the utmost care is taken to make the treatment rigorous at the mathematical level assumed. Every concept is properly defined and illustrated with examples and counter examples. The important points are specifically made in ' comments ' following the examples. A sufficient number of problem for a complete understanding of the topics discussed is given at the end of each section, and an additional set of problems appears at the end of each chapter, some of which supplement the theory in that chapter. Answers to these problems are provided at the end of the book. Also a number of statistical decision problems are included following the discussion of mathematical expectation. Acceptance sampling and quality control problems are discussed after introducing probability models, with a view to giving some practical applications of the models. A brief introduction to the topic of entropy is also given. Other applications have been omitted to keep the book to a manageable size. All the important results, correspondences and relationships are given in tabular form for quick reference. Most of the illustrations are taken from daily life, keeping in mind the age group of students for whom the book is intended. Vl ## PREFACE It is suggested that the book be used for a twenty-five-week course of three hours per week, given as a first course in statistics for arts, science, commerce and engineering students. This could usefully be supplemented by an additional one-hour problems session each week for those students who have difficulty with the subject. Front Matter....Pages i-xv Front Matter....Pages xvii-xvii Statistical Populations and Sampling....Pages 1-55 An Outcome Set....Pages 56-80 Probability....Pages 81-106 Front Matter....Pages 107-107 A Stochastic Variable....Pages 109-144 Univariate Probability Models—Discrete....Pages 145-173 Univariate Probability Models—Continuous....Pages 174-200 Sampling Distributions....Pages 201-238 Front Matter....Pages 239-239 Statistical Estimation....Pages 241-263 Tests of Statistical Hypotheses....Pages 264-299 Some Non-Parametric Tests....Pages 300-326 Statistical Regression....Pages 327-341 Analysis of Variance....Pages 342-354 Back Matter....Pages 355-406