Computer Laboratory – Course material 2009

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Paper 2: Probability

This course is not taken by NST or PPST students.

Lecturer: Professor J.G. Daugman

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.

Next: Paper 2: Regular Languages Up: Easter Term 2010: Part Previous: Paper 1: Algorithms I Contents