Unit name | Probability and Statistics |
---|---|
Unit code | MATH10013 |
Credit points | 20 |
Level of study | C/4 |
Teaching block(s) |
Teaching Block 4 (weeks 1-24) |
Unit director | Professor. Johnson |
Open unit status | Not open |
Pre-requisites |
A in A Level Mathematics or equivalent |
Co-requisites |
None |
School/department | School of Mathematics |
Faculty | Faculty of Science |
Lecturers: Oliver Johnson (TB1) and Feng Yu (TB2)
Unit Aims
This unit introduces student to basic ideas and methods in the areas of Probability and Statistics. It aims to develop the concepts of random variables, expectations and variances and look at some simple applications of these ideas and methods. It will also introduce the role of statistics in contemporary applications and aims to develop an elementary understanding of, and fluency in, the statistical paradigm of data collection, exploration, modelling and inference.
Unit Description
Probability is an everyday concept of which most people have only a vague intuitive understanding. Study of games of chance, such as tossing dice and card games, 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. Today probability is a well established and actively researched area of mathematics with lively links to Analysis, Combinatorics, Functional Analysis, Game Theory, Geometry, Mathematical Physics, Statistics. It also serves as a very important basis which various disciplines build on (Biology, Computer Science, Economics, Engineering, Linguistics, Physics, Sociology, just to mention a few).
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) and techniques are developed for evaluating these quantities, including generating functions and conditional expectations.
Computer technology has revolutionised both the scope and method of statistics, and the second half of this unit aims to give a basic grounding in statistical methodology that reflects this contemporary view. The role of statistics in the modern world is becoming ever-wider and applications can be found in almost all fields of human endeavour - in science, medicine, industry, social science, commerce and government. Taking real-life examples as motivation, this unit aims to develop an understanding of the basic principles of statistics, combining exploratory techniques and the machinery of probability theory to build a toolkit that can be used to uncover and identify relationships in the presence of random variation.
Relation to Other Units
This unit provides the foundation for all probability and statistics units in later years.
Students should be able to:
The unit will be taught through a combination of
Assessment for learning/Formative assessment:
Assessment of learning/Summative assessment:
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