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Probability and Statistical Inference (Wiley Series in Probability and Statistics) (Hardcover)
Hardcover: 647 pages Publisher: Wiley-Interscience; 2 edition (January 2, 2008) Language: English Book Description
Probability and Statistical Inference, Second Edition is a user-friendly book that stresses the comprehension of concepts instead of the simple acquisition of a skill or tool. It provides a mathematical framework that permits students to carry out various procedures using any number of computer software packages as opposed to relying on one particular package. Its unique approach to problems allows readers to integrate the knowledge gained from the text, thus, enhancing a more complete and honest understanding of the topic.
Book Info
Emphasizes theoretical comprehension rather than the narrow acquisition of concepts or skills. Focuses on the development of intuition and understanding through diversity of experience. DLC: Probabilities. --This text refers to the edition.CONTENTS
Preface
1 Experiments, Sample Spaces, and Events
1.1 Introduction
1.2 Sample Space
1.3 Algebra of Events
1.4 Infinite Operations on Events
Probability
2.1 Introduction
2.2 Probability as a Frequency
2.3 Axioms of Probability
2.4 Consequences of the Axioms
2.5 Classical Probability
2.6 Necessity of the Axioms*
2.7 Subjective Probability*
3 Counting 47
3.1 Introduction
3.3 Binomial Coefficients
3.4 Extension of Newton’s Formula
3.5 hlultinomial Coefficients
Product Sets, Orderings, and Permutations
4 Conditional Probability: Independence
4.1 Introduction
4.2 Conditional Probability
4.3 Partitions; Total Probability Formula
4.4 Bayes’ Formula
4.5 Independence
4.6 Exchangeability; Conditional Independence
5 Markov Chains*
5 . 1 Introduction and Basic Definitions
5.2
5.3 n-Step Transition Probabilities
5.4 The Ergodic Theorem
5.5 Absorption Probabilities
Definition of a Markov Chain
6 Random Variables: Univariate Case
6.1 Introduction
6.2 Distributions of Random Variables
6.3
6.4 Functions of Random Variables
6.5 Survival and Hazard Functions
Discrete and Continuous Random Variables
7 Random Variables: Multivariate Case
7.1 Bivariate Distributions
7.2 Marginal Distributions; Independence
7.3 Conditional Distributions
7.4 Bivariate Transformations
7.5 Multidimensional Distributions
8 Expectation
8.1 Introduction
8.2 Expected Value
8.3 Expectation as an Integral*
8.4 Properties of Expectation
8.5 Moments
8.6 Variance
8.7 Conditional Expectation
8.8 Inequalities
9Selected Families of Distributions
9.2 Hypergeometric Distribution
9.5 Normal Distribution
9.6 Beta Distribution
Bernoulli Trials and Related Distributions
Poisson Distribution and Poisson Process
Exponential, Gamma and Related Distributions
10Random Samples
10.1 Statistics and their Distributions
10.2 Distributions Related to Normal
10.3 Order Statistics
10.4 Generating Random Samples
10.5 Convergence
10.6 Central Limit Theorem
11 Introduction to Statistical Inference
11.1 Overview
11.2 Descriptive Statistics
11.3 Basic Model
11.4 Bayesian Statistics
11.5 Sampling
11.6 Measurement Scales
12Estimation
12.1 Introduction
12.2 Consistency
12.3 Loss, Risk, and Admissibility
12.4 Efficiency
12.5 Methods of Obtaining Estimators
12.6 Sufficiency
12.7 Interval Estimation
13 Testing Statistical Hypotheses
13.1 Introduction
13.2 Intuitive Background
13.3 Most Powerful Tests
13.4 Uniformly Most Powerful Tests
13.5 Unbiased Tests
13.6 Generalized Likelihood Ratio Tests
13.7 Conditional Tests
13.8 Tests and Confidence Intervals
13.9 Review of Tests for Normal Distributions
13.10 Monte Carlo, Bootstrap, and Permutation Tests
14 Linear Models
14.1 Introduction
14.2
14.3 Distributional Assumptions
14.4
14.5 Testing Linearity
14.6 Prediction
14.7 Inverse Regression
14.8 BLUE
14.9 Regression Toward the Mean
14.10 Analysis of Variance
14.11 One-way Layout
14.12 Two-way Layout
14.13 ANOVA Models with Interaction
14.14 Further Extensions
Regression of the First and Second Kind
Linear Regression in the Normal Case
15 Rank Methods
15.1 Introduction
15.2 Glivenko-Cantelli Theorem
15.3 Kolmogorov-Smirnov Tests
15.4 One-Sample Rank Tests
15.5 Two-Sample Rank Tests
15.6 Kruskal-Wallis Test
16 Analysis of Categorical Data
16.1 Introduction
16.2 Chi-square Tests
16.3 Homogeneity and Independence
16.4 Consistency and Power
16.5 2 x 2 Contingency Tables
16.6 r x c Contingency Tables
Statistical Tables
Bibliography
Answers to Odd-Numbered Problems
Index 642