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MODULE SPECIFICATION – UNDERGRADUATE PROGRAMMES KEY FACTS Module name Module code School Department or equivalent UK credits ECTS Level Delivery location (partnership programmes only) Introduction to Probability and Statistics MA1608 School of Engineering and Mathematical Sciences Mathematical Sciences 15 7.5 4 MODULE SUMMARY Module outline and aims This module will provide you with the fundamental tools in probability and statistics which are part of the basic knowledge required for mathematicians, and necessary for the understanding of related modules later in the programme. The aims of the module are to Provide an introduction to probability. Provide an introduction to the analysis of data and statistical modelling. Content outline Ways of displaying data: bar chart, pie chart, stem-and-leaf plot, histogram. Summary statistics: mean, median, mode, variance, quartiles. Grouped data: summary statistics and cumulative frequencies. Paired data: covariance and correlation, linear regression and best fit. Randomness and the sample space; events using basic set theory. Conditional probability and independence. Discrete random variables, their associated statistics, and some models. Continuous random variables: basic properties, the normal distribution and the normal approximation to the Binomial distribution. Expectation and variance of combinations of independent variables and of samples. Confidence intervals. Parametric hypothesis testing. WHAT WILL I BE EXPECTED TO ACHIEVE? On successful completion of this module, you will be expected to be able to: Knowledge and understanding: Demonstrate an understanding of the axioms of probability and the definition of conditional probability. Understand the concept of a random variable and be familiar with common distributions. Know the definitions of common sample statistics. Understand the theory underlying statistical techniques. Skills: Construct probabilistic models appropriate to a problem described in words. Construct statistical displays appropriate to the data. Use Venn diagrams to illustrate probabilistic arguments. Explain in words the results of probabilistic or statistical analysis having regard to the situation being modelled. Apply mathematical tools in the analysis of problems in probability or statistics. Use statistical tables. Test hypotheses and derive confidence intervals in well defined circumstances. Values and attitudes: Demonstrate awareness of the need for caution in making claims based on statistical evidence and scepticism in interpreting the claims made by others. HOW WILL I LEARN? Teaching and Learning methods are designed to foster your knowledge of and enthusiasm for the subject and stimulate engagement and participation in the learning process. They encourage learning in depth and encourage you to reflect on and take responsibility for your own learning and to develop your academic self-confidence. Lectures are the principal introduction to new material. They are relatively formal in style and are presented to the whole student. Each lecture is of 50 minutes duration with the timetable based on units of one hour to allow for short breaks. Full, prompt attendance is expected. For tutorials, groups are smaller and provide opportunities for you to work on problems and exercises connected with the module. They also provide an additional opportunity for staff to help you with questions arising from the lectures. In addition to the taught elements of the programme, there will be the need for private study. This time will be spent working on background reading, revision of notes, work on tutorial problems, and preparation of the set exercises. Key learning and teaching resources will be put on the module website on Moodle. Teaching pattern: Teaching component Teaching type Contact hours (scheduled) Lectures Tutorials Lecture Tutorial Totals Placemen t hours 20 10 Self-directed study hours (independent ) 100 20 0 0 Total student learning hours 120 30 30 120 0 150 WHAT TYPES OF ASSESSMENT AND FEEDBACK CAN I EXPECT? Assessments The assessment for this module is by a 2 hour examination together with a series of set exercises. The set exercises will normally consist of questions to be completed during periods of self-study and a combination of different types of quizzes. Assessment pattern: Assessment component Assessment type Set Exercises Set Exercises Examination Written Exam Reassessment Task Written Exam Weighting 20 80 100 Minimum qualifying mark 0 0 40 Pass/Fail? N/A N/A N/A Assessment criteria Assessment Criteria are descriptions of the skills, knowledge or attributes students need to demonstrate in order to complete an assessment successfully and Grade-Related Criteria are descriptions of the skills, knowledge or attributes students need to demonstrate to achieve a certain grade or mark in an assessment. Assessment Criteria and Grade-Related Criteria for module assessments will be made available to students prior to an assessment taking place. More information will be available from the module leader. Feedback on assessment Following an assessment, students will be given their marks and feedback in line with the Assessment Regulations and Policy. More information on the timing and type of feedback that will be provided for each assessment will be available from the module leader. Assessment Regulations The Pass mark for the module is 40%. The weighting of the different components can also be found in the table above. The Programme Specification contains information on what happens if you fail an assessment component or the module. INDICATIVE READING LIST The book chosen to accompany this module is Introduction to Probability and Statistics by Seymour Lipschutz and John Schiller, in the Schaums Outlines series, published by McGraw-Hill. Alternatives are: Milton and Arnold: Introduction to Probability and Statistics (McGraw-Hill International Edition) Clarke and Cooke: A Basic Course in Statistics by Clarke and Cooke (Arnold). Daly, Hand, Jones, Lunn and McConway: Elements of Statistics (Addison Wesley, Open University) Version: 3.0 Version date: May 2016 For use from: 2016-17 Appendix: see http://www.hesa.ac.uk/content/view/1805/296/ for the full list of JACS codes and descriptions CODES HESA Code 122 Description Mathematics Price Group C JACS Code G300 Description The study of the collection and analysis of numerical data. The mathematical study of chance. Percentage (%) 50 G320 50