Models for Probability and Statistical Inference / Wiley Series in Probability and Statistics (PDF)

This concise, yet thorough, book is enhanced with simulations and
graphs to build the intuition of readers

Models for Probability and Statistical Inference was written over a
five-year period and serves as a comprehensive treatment of the
fundamentals of probability and statistical inference. With
detailed theoretical coverage found throughout the book, readers
acquire the fundamentals needed to advance to more specialized
topics, such as sampling, linear models, design of experiments,
statistical computing, survival analysis, and bootstrapping.

Ideal as a textbook for a two-semester sequence on probability and
statistical inference, early chapters provide coverage on
probability and include discussions of: discrete models and random
variables; discrete distributions including binomial,
hypergeometric, geometric, and Poisson; continuous, normal, gamma,
and conditional distributions; and limit theory. Since limit theory
is usually the most difficult topic for readers to master, the
author thoroughly discusses modes of convergence of sequences of
random variables, with special attention to convergence in
distribution. The second half of the book addresses statistical
inference, beginning with a discussion on point estimation and
followed by coverage of consistency and confidence intervals.
Further areas of exploration include: distributions defined in
terms of the multivariate normal, chi-square, t, and F (central and
non-central); the one- and two-sample Wilcoxon test, together with
methods of estimation based on both; linear models with a linear
space-projection approach; and logistic regression.

Each section contains a set of problems ranging in difficulty from
simple to more complex, and selected answers as well as proofs to
almost all statements are provided. An abundant amount of figures
in addition to helpful simulations and graphs produced by the
statistical package S-Plus(r) are included to help build the
intuition of readers.