Probability and Statistical Inference

Presents the rigorous theory of probability and statistical inference in the style of a tutorial, using worked examples, exercises, numerous figures and tables, and computer simulations to develop and illustrate concepts. This book covers various topics typically addressed in a two-semester course in probability and statistical inference.

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Priced very competitively compared with other textbooks at this level!
This gracefully organized textbook reveals the rigorous theory of probability and statistical inference in the style of a tutorial, using worked examples, exercises, numerous figures and tables, and computer simulations to develop and illustrate concepts.

Beginning with an introduction to the basic ideas and techniques in probability theory and progressing to more rigorous topics, Probability and Statistical Inference

studies the Helmert transformation for normal distributions and the waiting time between failures for exponential distributions

develops notions of convergence in probability and distribution

spotlights the central limit theorem (CLT) for the sample variance

introduces sampling distributions and the Cornish-Fisher expansions

concentrates on the fundamentals of sufficiency, information, completeness, and ancillarity

explains Basu's Theorem as well as location, scale, and location-scale families of distributions

covers moment estimators, maximum likelihood estimators (MLE), Rao-Blackwellization, and the Cramér-Rao inequality

discusses uniformly minimum variance unbiased estimators (UMVUE) and Lehmann-Scheffé Theorems

focuses on the Neyman-Pearson theory of most powerful (MP) and uniformly most powerful (UMP) tests of hypotheses, as well as confidence intervals

includes the likelihood ratio (LR) tests for the mean, variance, and correlation coefficient

summarizes Bayesian methods

describes the monotone likelihood ratio (MLR) property

handles variance stabilizing transformations

provides a historical context for statistics and statistical discoveries

showcases great statisticians through biographical notes

Employing over 1400 equations to reinforce its subject matter, Probability and Statistical Inference is a groundbreaking text for first-year graduate and upper-level undergraduate courses in probability and statistical inference who have completed a calculus prerequisite, as well as a supplemental text for classes in Advanced Statistical Inference or Decision Theory.