A course in probability and statistics
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Bibliographic Information
A course in probability and statistics
Duxbury Press, c1996
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Includes index
Description and Table of Contents
Description
This author's modern approach is intended primarily for honors undergraduates or undergraduates with a good math background taking a mathematical statistics or statistical inference course. The author takes a finite-dimensional functional modeling viewpoint (in contrast to the conventional parametric approach) to strengthen the connection between statistical theory and statistical methodology.
Table of Contents
1. RANDOM VARIABLES AND THEIR DISTRIBUTION
Introduction / Sample Distributions / Distributions / Random Variables / Probability Functions and Density Functions / Distribution Functions and Quantiles / Univariate Transformations / Independence
2. EXPECTATION
Introduction / Properties of Expectation / Variance / Weak Law of Large Numbers Simulation and the Monte Carlo Method
3. SPECIAL CONTINUOUS MODELS
Gamma and Beta Distributions / The Normal Distribution / Normal Approximation and the Central Limit Theorem
4. SPECIAL DISCRETE MODELS
Combinatorics / The Binomial Distribution / The Multinomial Distribution / The Poisson Distribution / The Poisson Process
5. DEPENDENCE
Covariance, Linear Prediction, and Correlation / Multivariate Expectation / Covariance and Variance - Covariance Matrices / Multiple Linear Prediction / Multivariate Density Function / Invertible Transformations / The Multivariate Normal Distribution
6. CONDITIONAL DISTRIBUTIONS
Sampling Without Replacement / Hypergeometric Distribution / Conditional Density Functions / Conditional Expectation / Prediction / Conditioning and the Multivariate Normal Distribution / Random Parameters
7. NORMAL MODELS
Introduction / Chi-Square, t, and F Distribution / Confidence Intervals / The t Test of an Inequality / The t Test of an Equality
8. THE F TEST
Introduction to Linear Regression / The Method of Least Squares / Factorial Experiments / Input-Response and Experimental Models
9. LINEAR ANALYSIS
Linear Spaces / Identifiability / Saturated Spaces / Inner Products / Orthogonal Projections / Normal Equations
10. LINEAR REGRESSION
Least-Square Estimation / Sums of Squares / Distribution Theory / sugar Beet Experiment / Lube Oil Experiment / The t Test / Submodels / The F Test
11. ORTHOGONAL ARRAYS
Main Effects / Interactions / Experiments with Factors Having Three Levels / Randomization, Blocking, and Covariates
12. BINOMIAL AND POISSON MODELS
Nominal Confidence Intervals and Tests / Exact P-values / One-Parameter Exponential Families
13. LOGISTIC REGRESSION AND POISSON REGRESSION
Input-Response and Experimental Models / Maximum-Likelihood Estimation / Existence and Uniqueness of the Maximum-Likelihood Estimate / Interactively Reweighted Least-Squares Method / Normal Approximation / The Likelihood-Ratio Test / APPENDICES: A. PROPERTIES OF VECTORS AND MATRICES / B. SUMMARY OF PROBABILITY / C. SUMMARY OF STATISTICS / D. HINTS AND ANSWERS / E. TABLES / INDEX
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