An introduction to probability theory and mathematical statistics / Vijay K. Rohatgi and A.K.Md. Ehsanes Saleh.
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...
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Full Text (via ProQuest) |
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| Format: | eBook |
| Language: | English |
| Published: |
Hoboken, New Jersey :
John Wiley & Sons, Inc.,
[2015]
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| Edition: | 3rd edition. |
| Series: | Wiley series in probability and statistics.
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Table of Contents:
- 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.