Probability and Statistical Inference

This textbook provides a detailed exploration of probability and statistical inference concepts, making it ideal for graduate and advanced undergraduate students.

This textbook offers a comprehensive exploration of the rigorous theory of probability and statistical inference, presented in a tutorial style. Probability and Statistical Inference employs worked examples, exercises, and a wealth of figures and tables to clarify complex concepts. Additionally, it integrates computer simulations to enhance understanding, making it an invaluable resource for students. Covering a broad range of topics typically found in a two-semester course, the book is designed to cater to both first-year graduate students and upper-level undergraduates who have a calculus background.

Beginning with foundational ideas in probability theory, the text progresses to more advanced subjects, including the Helmert transformation for normal distributions and the study of waiting times between failures in exponential distributions. It emphasizes essential concepts such as convergence in probability and distribution, as well as the central limit theorem (CLT) for sample variance. The book also delves into sampling distributions, sufficiency, information, and completeness, ensuring a thorough grounding in statistical principles.

In addition to theoretical discussions, Probability and Statistical Inference covers practical applications such as maximum likelihood estimators (MLE), uniformly minimum variance unbiased estimators (UMVUE), and hypothesis testing through the Neyman-Pearson framework. With over 1400 equations and a historical context that highlights significant statisticians, this text is not only educational but also engaging, making it a key resource for anyone serious about mastering the field of statistics.