An Introduction to probability and statistical inference 1st Edition by George Roussas ISBN 0125990200 978-0125990202

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Product details: 

ISBN 10: 0125990200 

ISBN 13: 978-0125990202

Author:  George G. Roussas

Roussas introduces readers with no prior knowledge in probability or statistics, to a thinking process to guide them toward the best solution to a posed question or situation. An Introduction to Probability and Statistical Inference provides a plethora of examples for each topic discussed, giving the reader more experience in applying statistical methods to different situations. “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 mixture between conversational tones and formal mathematics; the appropriate combination for a math text at [this] level. In my examination I could find no instance where I could improve the book.” ― H. Pat Goeters, Auburn, University, Alabama

* Contains more than 200 illustrative examples discussed in detail, plus scores of numerical examples and applications* Chapters 1-8 can be used independently for an introductory course in probability* Provides a substantial number of proofs

Table of contents: 

1 SOME MOTIVATING EXAMPLES AND SOME FUNDAMENTAL CONCEPTS
1.1 Some Motivating Examples
1.2 Some Fundamental Concepts
1.3 Random Variables

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

3 NUMERICAL CHARACTERISTICS OF A RANDOM VARIABLE, SOME SPECIAL RANDOM VARIABLES
3.1 Expectation, Variance, and Moment Generating Function of a Random Variable
3.2 Some Probability Inequalities
3.3 Some Special Random Variables
3.4 Median and Mode of a Random Variable

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 Variables
4.5 The Multinomial, the Bivariate Normal, and the Multivariate Normal Distributions

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

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

7 SOME MODES OF CONVERGENCE OF RANDOM VARIABLES, APPLICATIONS
7.1 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

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

9 POINT ESTIMATION
9.1 Maximum Likelihood Estimation: Motivation and Examples
9.2 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

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, σ²) in the N(μ, σ²) Distribution
10.4 Confidence Intervals with Approximate Confidence Coefficient

11 TESTING HYPOTHESES
11.1 General Concepts, Formulation of Some Testing Hypotheses
11.2 Neyman–Pearson Fundamental Lemma, Exponential Type Families, Uniformly Most Powerful Tests for Some Composite Hypotheses
11.3 Some Applications of Theorems 2 and 3
11.4 Likelihood Ratio Tests

12 MORE ABOUT TESTING HYPOTHESES
12.1 Likelihood Ratio Tests in the Multinomial Case and Contingency Tables
12.2 A Goodness-of-Fit Test
12.3 Decision-Theoretic Approach to Testing Hypotheses
12.4 Relationship Between Testing Hypotheses and Confidence Regions

13 A SIMPLE LINEAR REGRESSION MODEL
13.1 Setting-up the Model — The Principle of Least Squares
13.2 The Least Squares Estimates of β₁ and β₂, and Some of Their Properties
13.3 Normally Distributed Errors: MLE’s of β₁, β₂, and σ², Some Distributional Results
13.4 Confidence Intervals and Hypotheses Testing Problems
13.5 Some Prediction Problems
13.6 Proof of Theorem 5
13.7 Concluding Remarks

14 TWO MODELS OF ANALYSIS OF VARIANCE
14.1 One-Way Layout with the Same Number of Observations per Cell
14.2 A Multicomparison Method
14.3 Two-Way Layout with One Observation per Cell

15 SOME TOPICS IN NONPARAMETRIC INFERENCE
15.1 Some Confidence Intervals with Given Approximate Confidence Coefficient
15.2 Confidence Intervals for Quantiles of a Distribution Function
15.3 The Two-Sample Sign Test
15.4 The Rank Sum and the Wilcoxon–Mann–Whitney Two-Sample Tests
15.5 Nonparametric Curve Estimation

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