Computer Laboratory

Course pages 2011–12


Paper 2: Probability

This course is not taken by NST or PPST students.

Lecturer: Dr R.J. Gibbens

No. of lectures: 8

Prerequisite course: Discrete Mathematics I

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. [2 lectures]

  • Multivariate distributions and independence. Random vectors and independence. Joint and marginal density functions. Variance, covariance and correlation. Conditional density functions. [2 lectures]

  • 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.

Recommended reading

* Grimmett, G. & Welsh, D. (1986). Probability: an introduction. Oxford University Press.