|Semester 1 Credit Value:||10|
|MAS1341||Introduction to Probability|
|MAS1342||Introduction to Statistics|
To acquire the mathematical and probabilistic skills necessary for the further study of statistics.
Probability is the branch of mathematics which helps us to describe, analyse and understand chance phenomena. While the development of competence in probability is an essential preparation for the study of modern statistics, probability is also an important object of study for pure mathematicians and plays a key role in many areas of applied mathematics. Perhaps the most remarkable thing we discover is that even random objects demonstrate regular patterns of behaviour which can helpfully be thought of as laws of probability.
Frequently we need to examine two or more variables at a time. Although we could study each random variable of interest separately, it may be more useful to study them jointly in order to discover relationships between them.
In the course we develop properties of probability distributions and present techniques which enable random variables to be transformed or combined. Important applications of probability are discussed and some remarkable general results derived.
Review of probability; conditional probability and independence; discrete and continuous random variables; simulation and probability integral transform; bivariate distributions; covariance and correlation; expectation; probability and moment generating functions. Illustrations will be carried out using the statistical package R.
Students will gain familiarity with a range of discrete and continuous probability laws, and will learn how to compute moments of random variables and the distributions of transformed random variables. Students will have some knowledge of bivariate distributions, correlation and covariance, expectation, moment and probability generating functions.
Students will be able to understand, use and calculate probabilities and expectations for a range of bivariate distributions. They will also be able to work with probability and moment generating functions. They will be able to use bivariate integration for joint distributions. They will be able to use R to analyse joint distributions and transformations of random variables.
|Graduate Skills Framework Applicable:||Yes|
|Scheduled Learning And Teaching Activities||Lecture||2||1:00||2:00||Revision lectures|
|Scheduled Learning And Teaching Activities||Lecture||6||1:00||6:00||Problem classes|
|Guided Independent Study||Assessment preparation and completion||1||11:00||11:00||Revision for unseen Exam|
|Guided Independent Study||Assessment preparation and completion||1||1:30||1:30||Unseen Exam|
|Guided Independent Study||Assessment preparation and completion||2||3:00||6:00||Revision for class test|
|Scheduled Learning And Teaching Activities||Lecture||22||1:00||22:00||Formal lectures|
|Guided Independent Study||Assessment preparation and completion||2||1:00||2:00||Class test|
|Guided Independent Study||Assessment preparation and completion||2||6:00||12:00||Written assignments and CBAs|
|Scheduled Learning And Teaching Activities||Practical||2||1:00||2:00||N/A|
|Scheduled Learning And Teaching Activities||Drop-in/surgery||6||1:00||6:00||Drop-ins in the lecture room|
|Guided Independent Study||Independent study||2||1:00||2:00||Assignment review|
|Guided Independent Study||Independent study||1||27:30||27:30||Studying, practising and gaining understanding of course material|
|MAS3304||Foundations of Probability|
Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem Classes are used to help develop the students’ abilities at applying the theory to solving problems. Drop-ins are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. Practicals are used both for solution of problems and work requiring extensive computation and to give insight into the ideas/methods studied. Office hours provide an opportunity for more direct contact between individual students and the lecturer.
The format of resits will be determined by the Board of Examiners
|Module Code||Module Title||Semester||Comment|
|MAS3304||Foundations of Probability||1||N/A|
|Prob solv exercises||1||M||10||Written assignments and computer based assessments|
|Prob solv exercises||1||M||10||Coursework tests|
A substantial formal unseen examination is appropriate for the assessment of the material in this module. Coursework assignments (approximately 2 assignments of approximately equal weight) and two coursework tests (in class) allow the students to develop their problem solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; this is thus formative as well as summative assessment. The coursework assignments may be written assignments, computer based assessments or a combination of the two, and in the case of combined assessments the deadlines for the two parts will not necessarily be the same.
Note: The Module Catalogue now reflects module information relating to academic year 15/16. Please contact your School Office if you require module information for a previous academic year.
Disclaimer: The University will use all reasonable endeavours to deliver modules in accordance with the descriptions set out in this catalogue. Every effort has been made to ensure the accuracy of the information, however, the University reserves the right to introduce changes to the information given including the addition, withdrawal or restructuring of modules if it considers such action to be necessary.