Statistics Prerequisite for Math Stat I and II
These are the topics from statistics with which students will be expected to be familiar. If a student is unfamiliar with a few of these, supplementary reading from an undergraduate statistics text will be suggested.
- Familiarity with basic ideas about sampling and experimental design.
- Use and interpretation of confidence intervals and hypothesis tests.
- Power calculations for hypothesis tests. ((Early in the first semester, one example will be provided and supplemental reading suggested for those who have not studied this before. It is essential that students understand this before beginning a discussion of optimality results for hypothesis tests.)
- Sampling distributions of sample means, sample proportions, and minimum and maximum statistics. Preferably this will have included derivations based on probability theory, including moment generating functions. (This material will be covered in detail again in Math Stat I, focusing on the more difficult parts.)
- Finding maximum likelihood estimators. (In Math Stat II, when we cover maximum likelihood estimation, we will focus on the more difficult problems, with little emphasis on the straightforward problems.)
- Comparison of estimators, using bias and comparison of variances. (In Math Stat I, we will briefly review these topics and in Math Stat II, will cover them in more detail, focusing on various optimality results.)