Aims - This module aims to provide an accessible and application-oriented introduction to basic ideas in probability and statistics. Together with STAT0003 and STAT0004, it provides the foundation for further study of statistics in the undergraduate degree programmes offered by the Department of Statistical Science or jointly with other departments. It also serves as a foundation module for students considering the mathematics and statistics stream of the Natural Sciences degree.

Objectives - On successful completion of the module, a student should understand, at an intuitive level, the basic concepts in probability theory; be able to use fundamental laws of probability to solve simple problems; recognise simple situations in which standard univariate probability distributions may be useful, and apply results for these distributions as appropriate in these situations; be able to choose and apply appropriate simple techniques for the presentation and description of data; understand the concepts of a probability model and sampling variability; and be aware of the need to check assumptions made when using a given probability model.

Applications - This module motivates the use of probability and statistics in a wide range of application areas. Recent high-profile statistical applications in areas such as politics, road safety, space travel, public health and criminal justice are discussed. Smaller teaching examples come from astronomy, medicine, meteorology, education, genetics, finance and physics.  

Content - Idea and rules of probability via proportions in a population. Conditional probability, associated results and applications. Notion of independence. Simple distributions (binomial, geometric, Poisson, uniform, normal and exponential). Concepts of expectation and variance, simple rules (without proof). Examples of real investigations. Types of data, graphs, tables and summary statistics. Samples and populations. Probability models, unknown parameters, fitting models to data and assessing goodness of fit informally. Notion of uncertainty in estimation; illustration via simulation. Contingency tables (2- and 3-way), row and column proportions. Regression and correlation as bivariate descriptions: principle of least squares, use of transformations.

Key texts - Available from ReadingLists@UCL.