## Overview: The central limit theorem

The second project in the course is all about the central limit theorem, which is arguably the central theorem in statistics. Once again you learnt about this theorem in level one but this material is difficult so it bears repeating. The central idea idea that we are trying to get at with this part of the course concerns using probability theory to develop a numerical measure for the degree of confidence that we have in a particular (quantitative) statement. The simple version of this idea is that if we have two measurements of some quantity that are very similar we are more likely to believe that each of the individual measurements represent something close to the truth. We are mathematicians though so we would like to develop a more quantitative version of this intuition. This is what the central limit theorem allows us to do.

### Aims

• You should be able to explain the difference between systematic and random error.
• You should be able to state the central limit theorem and define all the terms in this theorem correctly.
• You should be able to calculate confidence limits that give a measure of the random error in the sample mean calculated from a set of indepdendent random variables.

### Contact Details

School of Mathematics and Physics,
Queen's University Belfast,
Belfast,
BT7 1NN

Email: g.tribello@qub.ac.uk
Website: mywebsite