Degrees	Moderations — Computer Science
Term	Michaelmas Term 2008  (8 lectures)

Overview

An understanding of random phenomena is becoming increasingly important in today's world within social and political sciences, finance, life sciences and many other fields. The aim of this introduction to probability is to develop the concept of chance in a mathematical framework. Discrete random variables are introduced, with examples involving most of the common distributions.

Learning outcomes

Students should have a knowledge and understanding of basic probability concepts, including conditional probability. They should know what is meant by a random variable, and have met the common distributions and their probability mass functions. They should understand the concepts of expectation and variance of a random variable. A key concept is that of independence which will be introduced for events and random variables.

Synopsis

Motivation, relative frequency, chance. (What do we mean by a 1 in 4 chance?) Sample space as the set of all possible outcomes�examples. Events and the probability function. Permutations and combinations, examples using counting methods, sampling with or without replacement. Algebra of events. Conditional probability, partitions of sample space, theorem of total probability, Bayes's Theorem, independence.

Random variable. Probability mass function. Discrete distributions: Bernoulli, binomial, Poisson, geometric, situations in which these distributions arise. Expectation: mean and variance. Probability generating functions, use in calculating expectations. Bivariate discrete distribution, conditional and marginal distributions. Extensions to many random variables. Independence for discrete random variables. Conditional expectation. Solution of linear and quadratic difference equations with applications to random walks.

Reading list

1. D. Stirzaker, Elementary Probability (CUP, 1994), Chapters 1�4, 5.1�5.6, 6.1�6.3, 7.1, 7.2, 7.4, 8.1, 8.3, 8.5 (excluding the joint generating function).
2. D. Stirzaker, Probability and Random Variables: A Beginner's Guide (CUP, 1999).

Further reading

1. J. Pitman, Probability (Springer-Verlag, 1993).
2. S. Ross, A First Course In Probability (Prentice-Hall, 1994).
3. G. R. Grimmett and D. J. A. Welsh, Probability: An Introduction (OUP, 1986), Chapters 1�4, 5.1�5.4, 5.6, 6.1, 6.2, 6.3 (parts of), 7.1�7.3, 10.4.

Taking our courses

This form is not to be used by students studying for a degree in the Department of Computer Science, or for Visiting Students who are registered for Computer Science courses

Other matriculated University of Oxford students who are interested in taking this, or other, courses in the Department of Computer Science, must complete this online form by 17.00 on Friday of 0th week of term in which the course is taught. Late requests, and requests sent by email, will not be considered. All requests must be approved by the relevant Computer Science departmental committee and can only be submitted using this form.