MS Course textbook

(The attached PDF file has better formatting.)

The textbook for the course is Modern Mathematical Statistics with Applications by Jay Devore and Kenneth Berk, 2nd edition (Springer Texts in Statistics, New York 2011) or 1st edition (Springer, New York 2007).

The textbook balances real-world practicability with mathematical rigor. It assumes competency in calculus and probability, but it focuses on understanding of statistical concepts, not just on the mathematical proofs. It uses examples drawn primarily from life sciences (ecology, medicine, genetics) and social sciences (marketing, public opinion, politics).

The textbook is attached to this posting.

The last two modules of this course apply the statistical methods to actuarial pricing and risk classification. The required readings are on the discussion forum.

No statistical software is required for the course, but you will master the material quicker if you reproduce the examples on a spread-sheet or other computer package. As you work through this course, check your work with spread-sheets (Excel), statistical packages, or internet sites.

Excel has built-in cumulative distribution functions for the normal distribution, t distribution, F distribution, and most other distributions used in this course. The Analysis ToolPak add-in for Excel reproduces several of the analyses (t tests, ANOVA, regression analysis) in the textbook. (The add-in comes with the Excel package.)

Read the Microsoft instructions: “Use the Analysis ToolPak to perform complex data analysis”:

https://support.office.com/en-us/article/use-the-analysis-toolpak-to-perform-complex-data-analysis-6c67ccf0-f4a9-487c-8dec-bdb5a2cefab6

Excel Easy explains the Analysis ToolPak on http://www.excel-easy.com/data-analysis/analysis-toolpak.html

The mathematical statistics course assumes knowledge of probability (as covered by actuarial Course P). The textbook covers both probability and statistics; only the statistics sections are tested on the final exam.

Several distributions are used in the statistics sections: the normal distribution, t distribution, χ2 distribution, F distribution, binomial distribution, Poisson distribution, logit distribution, and uniform distribution. Know the shape and attributes of these distributions; they are not tested directly on the final exam, but they are assumed by final exam problems. For example, probability plots (quantile comparison plots), which are tested on the final exam, depend on the shape of the distribution being compared to the normal distribution.

The mathematical statistics course assumes knowlege of the probability density function and the cumulative distribution function. The textbook also covers the moment generating function, which is not tested on the final exam and is not needed for this course (though it is included on the Course P syllabus).