Unit name | Probability 1 |
---|---|
Unit code | MATH11300 |
Credit points | 10 |
Level of study | C/4 |
Teaching block(s) |
Teaching Block 1 (weeks 1 - 12) |
Unit director | Professor. McNamara |
Open unit status | Not open |
Pre-requisites |
A good pass in A-level Maths or equivalent |
Co-requisites |
MATH11007 Calculus 1 |
School/department | School of Mathematics |
Faculty | Faculty of Science |
This unit introduces the basic ideas and methods of Probability. Some familiarity with calculus is needed. Probability is an everyday concept of which most people have only a vague intuitive understanding. Study of games of chance resulted in early attempts to formalise the theory; but a satisfactory rigorous basis for the subject only came with the axiomatic theory of Kolmogorov in 1933. The unit starts with the idea of a probability space, which is how we model the outcome of a random experiment. Probability models are then introduced in terms of random variables (which are functions of the outcomes of a random experiment), and the simpler properties of standard discrete and continuous random variables are discussed. Motivation is given for studying the common quantities of interest (probabilities, expected values, variances and covariances). Techniques are developed for evaluating these quantities, including generating functions, conditional expectations and simple approximate methods.
Aims:
To introduce the basic ideas and methods of Probability, developing the concepts of random variables, expectations and variances. To look at some simple applications of these ideas and methods.
Syllabus
Relation to Other Units
This unit provides the foundation for all probability and statistics units in later years.
When you have successfully completed this module you will be able to:
Define events and sample spaces, describe them in simple examples, and use counting arguments to calculate probabilities when there are equally likely outcomes.
Transferable Skills:
Model building. Especially the formal mathematical modelling of informal descriptions of events and processes.
Lectures supplemented (for first year students) by small group tutorials. Weekly problem sheets, with outline solutions handed out a fortnight later.
The final mark for Probability 1 is calculated from one 1½ -hour written examination in April. This examination paper is in two sections.
Calculators are not permitted in the examination.
September examinations
If you fail Probability 1 (or any other unit in the Science Faculty), you may be required to resit in September. Your departmental or Faculty handbook explains the conditions under which resits may be allowed. The September examinations have the same format as the April examination (given above).
The recommended text is:
S. M. Ross A First Course in Probability, Prentice Hall International A suitably abbreviated version of this text, at a reduced price, will be available.
The statistical software package R will be used during the course. This software is available on the computers in the undergraduate laboratory, and for home use is available to download for free from the R project homepage.