Course pages 2012–13

# Probability

**Principal lecturer:** Dr Richard Gibbens**Taken by:** Part IA CST**Past exam questions****Information for supervisors** (contact lecturer for access permission)

No. of lectures: 8

Suggested hours of supervisions: 3

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.

## 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. [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]

## 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.