STAT0002 Introduction to Probability and Statistics#

About: This module aims to provide an accessible and application-oriented introduction to basic ideas in probability and statistics. 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.

Highlights:

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.

STAT0002 concentrates on understanding important concepts, rather than formal mathematics, but also helps you to develop some skill in presenting basic mathematics arguements, especially the use of probabilistic arguements and analysis of data. This is immediatly followed by STAT0003, which considers more formally the ideas and methods introduced in STAT0002. Beyond that there are other Statistics modules that can be taken in year 2 and after.

Prerequisites: A-level Mathematics, or the equivalent, including: algebra and functions; exponentials and logarithms; differentiation and integration; sequences and series. We do not assume any prior knowledge of Probability or Statistics.

Contents (indicative):

  • 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

Recommended readings:

For a full reading list, click here.

Teaching:

  • Lectures

  • Tutorials

Assessment:

  • 75% Examination

  • 15% Examination

  • 10% Examination

You can also refer to the UCL Module Catalogue entry