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 the lifetime of light bulbs, or for the number of mistypings in 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 as well.
The module will be useful especially for those preparing to write STEP papers (applying to Cambridge or Imperial College London), because choosing questions from the Probability and Statistics part is an option there. We are going to solve some STEP questions in the module, too