Mathematical statistics is the application of probability theory to statistics. It is an important area that provides useful connections to other areas of mathematics and has applications across the sciences, business, government, and more. It is a core topic in the burgeoning field of data science.

In this module, you will build on your previous study of probability and statistics. You will engage with and extend the fundamentals of mathematical statistics, including probability, distribution theory, statistical estimation, models, and Bayesian methods, all with applications in R, an industry-standard programming language for statistical computing.

Topics include:

Probability, combinatorics, discrete and continuous random variables

Theory of discrete and continuous distributions

Transforming random variables

Sampling distributions. Random sampling. The central limit theorem.

The method of moments and the method of maximum likelihood.

Confidence intervals and hypothesis testing.

Simple linear regression and forms of correlation.