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A Course in Mathematical Statistics
A Course in Mathematical Statistics, Second Edition, contains enough material for a year-long course in probability and statistics for advanced undergraduate or first-year graduate students, or it can be used independently for a one-semester (or even one-quarter) course in probability alone. It bridges the gap between high and intermediate level texts so students without a sophisticated mathematical background can assimilate a fairly broad spectrum of the theorems and results from mathematical statistics. The coverage is extensive, and consists of probability and distribution theory, and statistical inference.
Concepts of Set Theory Some Probabilistic Concepts and Results On Random variables and Their Distributions Distribution Functions, Probability Densities, and their Relationships Moments of Random Variables-Some Moment and Probability Inequalities Characteristic Functions, Moment Generating Functions, and Related Theorems Stochastic Independence with Some Applications Basic Limit Theorems Transformations of Random Variables and Random Vectors Order Statistics and Related Theorems Sufficiency and Related Theorems Point Estimation Testing Hypotheses Sequential Procedures Confidence Regions-Tolerance Intervals The General Linear Hypothesis Analysis of Variance The Multivariate Normal Distribution Quadratic Forms Nonparametric Inference Appendices Table of Selected Discrete and Continuous Distributions and Some of their Characteristics Some Notation and Abbreviations