Introduction to probablility and statistical inference / George Roussas.

Format:

Book

Author/Creator:

Roussas, George G.

Language:

English

Subjects (All):

Probabilities.

Mathematical statistics.

Physical Description:

1 online resource (543 p.)

Place of Publication:

Amsterdam ; Boston : Academic Press, c2003.

Language Note:

English

Summary:

""The text is wonderfully written and has the mostcomprehensive range of exercise problems that I have ever seen."" - Tapas K. Das, University of South Florida""The exposition is great; a

Contents:

Cover; Contents; Preface; Chapter 1. SOME MOTIVATING EXAMPLES AND SOME FUNDAMENTAL CONCEPTS; 1.1 Some Motivating Examples; 1.2 Some Fundamental Concepts; 1.3 Random Variables; Chapter 2. THE CONCEPT OF PROBABILITY AND BASIC RESULTS; 2.1 Definition of Probability and Some Basic Results; 2.2 Distribution of a Random Variable; 2.3 Conditional Probability and Related Results; 2.4 Independent Events and Related Results; 2.5 Basic Concepts and Results in Counting; Chapter 3. NUMERICAL CHARACTERISTICS OF A RANDOM VARIABLE, SOME SPECIAL RANDOM VARIABLES

3.1 Expectation, Variance, and Moment Generating Function of a Random Variable3.2 Some Probability Inequalities; 3.3 Some Special Random Variables; 3.4 Median and Mode of a Random Variable; Chapter 4. JOINT AND CONDITIONAL P.D.F.'S, CONDITIONAL EXPECTATION AND VARIANCE, MOMENT GENERATING FUNCTION, COVARIANCE, AND CORRELATION COEFFICIENT; 4.1 Joint d.f. and Joint p.d.f. of Two Random Variables; 4.2 Marginal and Conditional p.d.f.'s, Conditional Expectation and Variance; 4.3 Expectation of a Function of Two r.v.'s, Joint and Marginal m.g.f.'s, Covariance, and Correlation Coefficient

4.4 Some Generalizations to k Random Variables4.5 The Multinomial, the Bivariate Normal, and the Multivariate Normal Distributions; Chapter 5. INDEPENDENCE OF RANDOM VARIABLES AND SOME APPLICATIONS; 5.1 Independence of Random Variables and Criteria of Independence; 5.2 The Reproductive Property of Certain Distributions; Chapter 6. TRANSFORMATION OF RANDOM VARIABLES; 6.1 Transforming a Single Random Variable; 6.2 Transforming Two or More Random Variables; 6.3 Linear Transformations; 6.4 The Probability Integral Transform; 6.5 Order Statistics

Chapter 7. SOME MODES OF CONVERGENCE OF RANDOM VARIABLES, APPLICATIONS7.1 Convergence in Distribution or in Probability and Their Relationship; 7.2 Some Applications of Convergence in Distribution: The Weak Law of Large Numbers and the Central Limit Theorem; 7.3 Further Limit Theorems; Chapter 8. AN OVERVIEW OF STATISTICAL INFERENCE; 8.1 The Basics of Point Estimation; 8.2 The Basics of Interval Estimation; 8.3 The Basics of Testing Hypotheses; 8.4 The Basics of Regression Analysis; 8.5 The Basics of Analysis of Variance; 8.6 The Basics of Nonparametric Inference; Chapter 9. POINT ESTIMATION

9.1 Maximum Likelihood Estimation: Motivation and Examples9.2 Some Properties of Maximum Likelihood Estimates; 9.3 Uniformly Minimum Variance Unbiased Estimates; 9.4 Decision-Theoretic Approach to Estimation; 9.5 Other Methods of Estimation; Chapter 10. CONFIDENCE INTERVALS AND CONFIDENCE REGIONS; 10.1 Confidence Intervals; 10.2 Confidence Intervals in the Presence of Nuisance Parameters; 10.3 A Confidence Region for (μ, s2) in the N(μ, s2) Distribution; 10.4 Confidence Intervals with Approximate Confidence Coefficient; Chapter 11. TESTING HYPOTHESES

11.1 General Concepts, Formulation of Some Testing Hypotheses

Notes:

Includes index.

ISBN:

1-281-01220-3

9786611012205

0-08-049575-3

OCLC:

437182263