Lecturer: Prof John Daugman
Taken by: Part IA CST
No. of lectures: 6
This course is a prerequisite for the Part IB course Mathematical Methods for Computer Science, and the following Part II
courses: Artificial Intelligence II, Computer Systems Modelling, Information Theory and Coding, Computer Vision, Digital
Signal Processing, Natural Language Processing and Information Retrieval.
The main aim of this course is to provide a foundation in
Probability with emphasis on areas that are particularly applicable
to Computer Science.
- Review of elementary probability theory. Random
variables. Discrete and continuous distributions. Means and
variances, moments, independence, conditional probabilities.
Bayes's theorem. [2 lectures]
- Probability generating functions. Definitions and
properties. Use in calculating moments of random variables and for
finding the distribution of sums of independent random
variables. [1 lecture]
- Multivariate distributions and independence. Random vectors
and independence. Joint and marginal density functions. Variance,
covariance and correlation. Conditional density functions.
- Elementary stochastic processes. Random walks. Recurrence
and transience. The Gambler's Ruin problem. Solution using
difference equations. [2 lectures]
At the end of the course students should
- have a thorough understanding of concepts in probability theory and
a practical knowledge of associated calculations;
- be aware of applications of probability across the field of
* Grimmett, G. & Welsh, D. (1986). Probability: an introduction. Oxford University Press.
Past exam questions
Information for supervisors (contact lecturer for access permission)