Course material 2010–11
This course is not taken by NST or PPST students.
Lecturer: Dr R.J. Gibbens
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. [1 lecture]
- 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 computer science.
* Grimmett, G. & Welsh, D. (1986). Probability: an introduction. Oxford University Press.