# Mathematics

## Probability and Statistics

Module code: G5098
Level 5
15 credits in spring semester
Teaching method: Lecture, Workshop
Assessment modes: Group written submission, Coursework, Computer based exam

Topics covered on this module include:

• multivariate discrete and continuous distributions (topic includes expectations, covariance, lower dimensional marginals, distributions of sums of independent random variables and central limit theorem (CLT), transformations of random variables, introduction to statistical linear regression of uniform random samples and point estimators for mean and variance)
• conditional expectations
• multivariate normal distributions, multivariate CLT and introduction of basic statistics and statistical distributions, sample mean and variance, t; 2 and F distributions
• parameter estimation (exponential family of distributions, unbiased estimators, sucient estimators and maximum likelihood estimators, the German tank problem, Condence intervals)
• hypothesis testing (z- and t-tests, 2 tests, including Pearson's test and test for proportions, contingency tables).

### Module learning outcomes

• Deep understanding of vector random variables and (limiting) distributions of functions of random samples. In particular, knowledge of important distributions and their applications.
• Rigorous mathematical founding of statistics.
• Ability to apply statistical tests to data sets and correctly understand the results. In particular, the ability to estimate sample parameters (mean, variance, ... ) and infer further properties of the driving random variables.
• Ability to work within a group on a small project and write mathematics; in particular, training in mathematical writing and presentation of a statistical analysis of data sets to an expert/non-expert third party without sacrificing the rigor and precision.