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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.

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