Probability 2009–10
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.
Aims
The main aim of this course is to provide a foundation in
Probability with emphasis on areas that are particularly applicable
to Computer Science.
Lectures
 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]
Objectives
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.
Lecture Notes
Exercises
Past exam questions
Syllabus
Information for supervisors (contact lecturer for access permission)
