Probability II: 2008-2009
Degrees | |
Term | Hilary Term 2009 (8 lectures) |
Overview
NB. This course consists of 8 lectures, but straight Computer Science students not examined on Continuous Probability, and so are only expected to attend the first 4 lectures (but may attend the others if they wish)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 density 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. The emphasis on this course is a continuation of discrete variables studied in Probability I, followed by continuous random variables, with examples involving the common distributions.Synopsis
Random walks (finite state space only). Expectations of functions of more than one random variable. Random sample. Conditional expectation, application of theorem of total probability to expectation of a random variable. Sums of independent random variables. Examples from well-known distributions.
Continuous random variables, motivation. Cumulative distribution functions for both discrete and continuous random variables. Probability density function – analogy with mass and density of matter. Examples: uniform, exponential, gamma, normal. Practical examples. Expectation. Cdf and pdf for function of a single continuous random variable. Simple examples of joint distributions of two or more continuous random variables; independence, expectation (mean and variance of sums of independent, identically distributed random variables).
Reading list
- 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).
- D. Stirzaker, Probability and Random Variables: A Beginner's Guide (CUP, 1999).
Further reading
- J. Pitman, Probability (Springer-Verlag, 1993).
- S. Ross, A First Course In Probability (Prentice-Hall, 1994).
- 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.