Mathematical Statistics 1 - Class Notes
From Introduction to Mathematical Statistics 8th Edition, Robert Hogg, Joseph McKean, and Allan Craig (Pearson, 2019)
Hogg, McKean, and Craig's Introduction to Mathematical Statistics book, 8th edition

The catalog description for Mathematical Statistics 1 is: "An introduction to the theory of probability and mathematical statistics. Topics will include discrete and continuous probability distributions and their applications, mathematical expectation and moment generating functions, functions of random variables and transformations, sampling distributions, the central limit theorem, χ-square, t and F distributions." The prerequisites are Linear Algebra (MATH 2010), Foundations of Probability and Statistics-Calculus Based (MATH 2050), and Calculus 3 (MATH 2110). Notice that Mathematical Statistics 1 is a sufficient prerequisite for Mathematical Statistics 2 (STAT 4057/5057), Applications of Statistics (STAT 4287/5287), and Sampling and Survey Techniques (STAT 4307/5307).

Mathematical Statistics 2 deals more with the statistical concepts and the catalog description for it is: "A continuation of Mathematical Statistics I. An introduction to the theory of mathematical statistics, estimation, and hypothesis testing. Topics will include efficiency, consistency, sufficiency, robustness, methods of estimation, confidence intervals, Bayesian inference as well as the Neyman-Pearson lemma, power functions, likelihood ratio tests, hypothesis tests, and applications." These descriptions are based on the ETSU 2019-20 Undergraduate Catalog. More details about Mathematical Statistics 2 are on my Mathematical Statistics 2 - Class Notes webpage.

Author Joseph McKean has a HOMEPAGE for the 8th EDITION of HMC where auxillary and supplemental material (including information on the software R) for the book can be downloaded. In particular, there is a Mathematical Primer for the 8th Edition which covers some topics from calculus and analysis (the topic of multiple integration is central to this class) and an Errata Sheet for the 8th Edition.

Copies of the classnotes are on the internet in PDF format as given below. The notes and supplements may contain hyperlinks to posted webpages; the links appear in red fonts. The "Examples, Exercises, and Proofs" files were prepared in Beamer. The "Printout of Examples, Exercises, and Proofs" are printable PDF files of the Beamer slides without the pauses. These notes have not been classroom tested and may have typographical errors.

1. Probability and Distributions.

2. Multivariate Distributions.

3. Some Special Distributions.

5. Consistency and Limiting Distributions.

Additional Chapters and Appendices.


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