An Rohatgi, V. K. 1939- creator Saleh, A. K. Md. Ehsanes. text bibliography Electronic books. Electronic books. nju 2015 3rd edition. monographic eng

electronic resource

1 online resource. A well-balanced introduction to probability theory and mathematical statistics Featuring a comprehensive update, An Introduction to Probability and Statistics, Third Edition remains a solid overview to probability theory and mathematical statistics. Divided into three parts, the Third Edition begins by presenting the fundamentals and foundations of probability. The second part addresses statistical inference, and the remaining chapters focus on special topics. Featuring a substantial revision to include recent developments, An Introduction to Probability and Statistics, Third Edition also. Title Page; Copyright Page; CONTENTS; PREFACE TO THE THIRD EDITION; PREFACE TO THE SECOND EDITION; PREFACE TO THE FIRST EDITION; ACKNOWLEDGMENTS; ENUMERATION OF THEOREMS AND REFERENCES; CHAPTER 1 PROBABILITY; 1.1 INTRODUCTION; 1.2 SAMPLE SPACE; 1.3 PROBABILITY AXIOMS; 1.4 COMBINATORICS: PROBABILITY ON FINITE SAMPLE SPACES; 1.5 CONDITIONAL PROBABILITY AND BAYES THEOREM; 1.6 INDEPENDENCE OF EVENTS; CHAPTER 2RANDOM VARIABLES AND THEIR PROBABILITY DISTRIBUTIONS; 2.1 INTRODUCTION; 2.2 RANDOM VARIABLES; 2.3 PROBABILITY DISTRIBUTION OF A RANDOM VARIABLE; 2.4 DISCRETE AND CONTINUOUS RANDOM VARIABLES 2.5 FUNCTIONS OF A RANDOM VARIABLECHAPTER 3MOMENTS AND GENERATING FUNCTIONS; 3.1 INTRODUCTION; 3.2 MOMENTS OF A DISTRIBUTION FUNCTION; 3.3 GENERATING FUNCTIONS; 3.4 SOME MOMENT INEQUALITIES; CHAPTER 4MULTIPLE RANDOM VARIABLES; 4.1 INTRODUCTION; 4.2 MULTIPLE RANDOM VARIABLES; 4.3 INDEPENDENT RANDOM VARIABLES; 4.4 FUNCTIONS OF SEVERAL RANDOM VARIABLES; 4.5 COVARIANCE, CORRELATION AND MOMENTS; 4.6 CONDITIONAL EXPECTATION; 4.7 ORDER STATISTICS AND THEIR DISTRIBUTIONS; CHAPTER 5SOME SPECIAL DISTRIBUTIONS; 5.1 INTRODUCTION; 5.2 SOME DISCRETE DISTRIBUTIONS; 5.2.1 Degenerate Distribution 5.2.2 Two-Point Distribution5.2.3 Uniform Distribution on n Points; 5.2.4 Binomial Distribution; 5.2.5 Negative Binomial Distribution (Pascal or Waiting Time Distribution); 5.2.6 Hypergeometric Distribution; 5.2.7 Negative Hypergeometric Distribution; 5.2.8 Poisson Distribution; 5.2.9 Multinomial Distribution; 5.2.10 Multivariate Hypergeometric Distribution; 5.2.11 Multivariate Negative Binomial Distribution; 5.3 SOME CONTINUOUS DISTRIBUTIONS; 5.3.1 Uniform Distribution (Rectangular Distribution); 5.3.2 Gamma Distribution; 5.3.3 Beta Distribution; 5.3.4 Cauchy Distribution 5.3.5 Normal Distribution (the Gaussian Law)5.3.6 Some Other Continuous Distributions; 5.4 BIVARIATE AND MULTIVARIATE NORMAL DISTRIBUTIONS; 5.5 EXPONENTIAL FAMILY OF DISTRIBUTIONS; CHAPTER 6SAMPLE STATISTICS AND THEIR DISTRIBUTIONS; 6.1 INTRODUCTION; 6.2 RANDOM SAMPLING; 6.3 SAMPLE CHARACTERISTICS AND THEIR DISTRIBUTIONS; 6.4 CHI-SQUARE, t-, AND F-DISTRIBUTIONS: EXACT SAMPLINGDISTRIBUTIONS; 6.5 DISTRIBUTION OF (X,S2) IN SAMPLING FROM A NORMALPOPULATION; 6.6 SAMPLING FROM A BIVARIATE NORMAL DISTRIBUTION; CHAPTER 7BASIC ASYMPTOTICS: LARGE SAMPLE THEORY; 7.1 INTRODUCTION 7.2 modes of convergence7.3 weak law of large numbers; 7.4 strong law of large numbers; 7.5 limiting moment generating functions; 7.6 central limit theorem; 7.7 large sample theory; chapter 8parametric point estimation; 8.1 introduction; 8.2 problem of point estimation; 8.3 sufficiency, completeness and ancillarity; 8.4 unbiased estimation; 8.5 unbiased estimation (continued): a lower bound forthe variance of an estimator; 8.6 substitution principle (method of moments); 8.7 maximum likelihood estimators; 8.8 bayes and minimax estimation; 8.9 principle of equivariance Vijay K. Rohatgi and A.K.Md. Ehsanes Saleh. Includes bibliographical references and index. Probabilities Mathematical statistics Mathematical statistics Probabilities MATHEMATICS / Applied MATHEMATICS / Probability & Statistics / General Mathematical statistics Mathematics Probabilities QA273 519.5 Rohatgi, V. K., 1939- Hoboken, New Jersey : John Wiley & Sons, Inc., [2015] 3rd edition. (DLC) 2015004848 9781118799659 (ePub) 1118799658 (ePub) 9781118799680 (Adobe PDF) 1118799682 (Adobe PDF) 9781118799635 1118799631 2015005260 http://onlinelibrary.wiley.com/book/10.1002/9781118799635 http://onlinelibrary.wiley.com/book/10.1002/9781118799635 DLC 150206 20171025110349.0 ocn902986846 eng