The module covers major topics in probability theory and statistics. We will introduce theoretical concepts through simple experiments and games. We will then discuss some important probability distributions: what kind of distribution should we use for lifetimes and waiting times, or for the number of mistypings on the pages of a newspaper? How can we describe a probability distribution through distribution functions, density functions and characteristic functions? We will explore the law of large numbers in mathematical form and the central limit theorem, including why the Gaussian, or Normal, distribution is special. These concepts are also used in financial mathematics. Together, they form the basis of statistics, providing tools for interpreting the world around us through estimates and hypothesis testing. These methods are used in the social sciences and medicine as well. The module is highly recommended for students wishing to study Mathematics, Economics or other numerical sciences at university, while students interested in certain fields of the natural sciences are also welcome.
