The module covers major topics of probability theory and statistics (up to first-year university level). We will introduce theoretical concepts through simple experiments and games. Then we discuss some important probability distributions: what kind of distribution shall we use for lifetimes/waiting times, or for the number of mistypings in the pages of a newspaper, etc. How can we describe a probability distribution: distribution functions and density functions (and also characteristic functions). Law of large numbers in a mathematical formulation. Central limit theorem – or why the Gaussian (Normal) distribution is special. These concepts are used in financial mathematics. The above concepts form the basis of statistics: giving tools for appraising the world around us. Estimates, hypothesis testing. These are used in social sciences and medicine as well.
The module will be especially useful for those preparing to write STEP papers (applying to Cambridge or Imperial College London) because choosing questions from Probability and Statistics is an option there. We are going to solve some STEP questions in the module, too.