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## Paper 2: Probability

This Paper 2 course is taken by Part IA Computer Science Tripos students only.

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.

Aims

The main aim of this course is to provide a foundation course in Probability with particular emphasis to further applications in Computer Science.

Lectures

• Review of elementary probability theory. Random variables. Discrete and continuous distributions. Means and variances, 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 the concepts of probability and practical knowledge of associated calculations

• be aware of applications of probability across the field of modern computer science

Recommended reading

* Grimmett, G. & Welsh, D. (1986). Probability: an introduction. Oxford University Press.    Next: Paper 2: Regular Languages Up: Easter Term 2009: Part Previous: Paper 1: Algorithms I   Contents