Introductory description

This module runs in Term 2 and follows on from ST111 Probability A and is an optional module which leads to numerous statistical, probabilistic, operational research and econometrics courses. You may be interested in this module if you wish to undertake further statistics modules.

Pre-requisites: ST111 Probability A
Post-requisites: ST104 Statistical laboratory, ST202 Stochastic Processes, ST220 Introduction to Mathematical Statistics

This module is not available to students who have their home department in Statistics, who take an equivalent module. Students who are considering transferring to a course in Data Science, Mathematics & Statistics or MORSE at the end of their first year should take this module.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

1. The notion of a random variable and its distribution. Examples in both discrete and continuous settings. Probability mass functions and density functions. Cumulative distribution functions.
2. Joint distributions. Independence of random variables.
3. Expectation of random variables. Properties of expectation.
4. Variance and Chebyshev's inequality. Covariance and the Cauchy-Schwartz inequality.
5. Addition of independent random variables: convolutions. Generating functions, Moment generating functions and their use to compute convolutions.
6. Important families of distributions: Binomial, Poisson, negative Binomial, exponential, Gamma and Gaussian. Their properties, genesis and inter-relationships.
7. The law of large numbers and the Central limit theorem.

Learning outcomes

By the end of the module, students should be able to:

• Apply the theory of probability distributions, expectation, variance and covariance associated with random variables.
• Compute and apply generating functions for univariate random variables.
• Interpret problems and select appropriate distributions to create probability models.
• Apply the law of large numbers and the central limit theorem to probability models.

Indicative reading list

Durrett, Elementary Probability for Applications.
Grimmett and Walsh, Probability- An Introduction.
Grimmett and Stirzaker, One Thousand Exercises in Probability

View reading list on Talis Aspire

Subject specific skills

TBC

Transferable skills

TBC