The main goal is to uncover the mathematical machinery behind core probabilistic and statistical concepts and properties. Topics in the first half include set opeartions, laws of probability, conditional probability, common discrete and continuous distributions, sampling distributions, moment generating functions and law of large numbers. The second half of the course focuses on two fundamental concepts in statistical inference: estimation and hypothesis testing. Finally we introduce important topics including linear regression and analysis of variance.
We will start with an overview of some fundamentals of nonparametric statistics. Then we will consider in turn methods for a single sample, for two samples, and for multiple samples. This will be followed by discussion of correlation, concordance, and regression, as well as association and other related methods for categorical data. Finally, we will look at a variety of more "modern" nonparametric methods, such as the bootstrap and kernel density estimation.