Aims

To introduce and reinforce a range of concepts in probability and statistics with particular emphasis on illustrations in R, including methods that will be useful towards future project work. To reinforce the computing in R studied within MAS1608, and to move towards expectations of more independent programming.

Module summary

Computational methods are of great use in a wide range of applications of probability and statistics. This module builds on the probability and the use of R introduced at Stage 1. Students will be introduced to additional concepts and techniques, some of increasing mathematical and computational sophistication. In implementing these methods, students will attain a deeper understanding of foundational probability and statistics, increasing competence with mathematical/statistical computing, and an increasing ability to use such methods independently, towards project-orientated goals.

Outline Of Syllabus

Review of basic ideas in R: Vector and dataframe subsetting and manipulation, data summaries, functions and control statements. Review of probability ideas: illustrations of properties of univariate, bivariate and trivariate distributions in R, including use of conditional distributions. Transformations of random variables, with illustrations in R. Sampling distributions. Illustration of properties of hypothesis tests and confidence intervals.

Teaching Rationale And Relationship

The teaching methods are appropriate to allow students to develop a wide range of skills, from understanding basic concepts and facts to higher-order thinking. Practicals 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.

Assessment Rationale And Relationship

A substantial class test is appropriate for the assessment of the material in this module. The format will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes. The assurance of academic integrity forms a necessary part of the programme accreditation.

Exam problems may require a synthesis of concepts and strategies from different sections, while they may have more than one ways for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments 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; these assessments have a secondary formative purpose as well as their primary summative purpose.