This classic textbook builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. It covers all topics from a standard inference course including: distributions, random variables, data reduction, point estimation, hypothesis testing, and interval estimation. Features: The classic graduate-level textbook on statistical inference Develops elements of statistical theory from first principles of probability Written in lucid style accessible to anyone with some background in calculus Covers all key topics of a standard course in inference Hundreds of examples throughout to aid understanding Each chapter includes extensive set of graduated exercises Statistical Inference, Second Edition is primarily aimed at graduate students of statistics, but can be used by advanced undergraduate students majoring in statistics who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures, while less concerned with formal optimality considerations.