## Probability and Statistics

### Module aims

In this module you will have the opportunity to:

• use probability theory to model uncertainty
• design simple probabilistic models that facilitate prediction
• conduct sound scientific analysis of data
• use Bayesian inference to refine hypotheses

### Learning outcomes

Upon successful completion of this module you will be able to:

• Describe notions of probability in terms of sample spaces
• Define and use random variables
• Design simple probability models and estimate their parameters from data
• Construct confidence intervals
• Perform hypothesis tests and draw scientific conclusions
• Apply estimation and testing procedures

### Module syllabus

This module covers the following topics:

• Foundations of probability based on measurable sets
• Discrete random variables and their probability distributions
• Poisson processes
• Continuous random variables and their probability distributions
• Central Limit Theorem
• Generating functions and Laplace transforms
• Joint random variables
• Estimation
• Hypothesis Testing
• Bayesian inference

### Teaching methods

The mathematical techniques will be developed from first principles, so you will obtain a deep understanding of both the foundations of probability and statistics and their application. Numerous examples will be given throughout aimed at linking the theory with practice. The material will be taught through traditional lectures, backed up by assessed exercises designed to reinforce the material as it is taught. There will be small-group tutorials, which you can join on a voluntary basis, run by Graduate Teaching Assistants (GTAs).

The Piazza Q&A web service will be used as an open online discussion forum for the module.

### Assessments

There will be a number of small assessed exercises throughout the term designed to reinforce the material as it is taught. These collectively count for 15% of the marks for the module. There will be a final written exam, which counts for the remaining 85% of the marks.

Written feedback will be given on the assessed exercises and this will normally be returned within one week of submission. If you elect to attend the small-group tutorials then you will also get regular additional verbal feedback and will benefit from the group discussions.