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AM10SP Level: 4 STATISTICS AND PROBABILITY Credits: 10 Teaching Period: 1 Module Tutors: Dr J van Mourik Aims Students should understand the general principles of probability and statistics. They should be able to: solve problems concerning elementary probability and random variables summarise and present data in a meaningful way. calculate confidence limits for sampled data perform tests of hypotheses concerning the mean, variance, goodness of fit, and contingency tables. perform linear regression. Content: Probability: 1. An introduction to probability: Sample description spaces; events spaces; Venn diagrams; Combinatorics. The axioms of probability. Definition and rules for combining probabilities. 2. Probability density functions: definition, cumulative, joint, marginal, independence, discrete and continuous random variables. Statistics: 3. Methods for summarising the data; histograms, measures of location, measures of central tendency, measures of spread. 4. Bias, minimum variance. 5. Estimation. Sampling distributions of x and S2. Confidence limits. Tests of hypothesis concerning the mean. Test of hypotheses concerning the variance. The χ 2 test for goodness of fit and contingency tables. 6. An introduction to covariance and correlation and linear regression: model fitting and significance tests. Teaching: Lectures 22 hours Tutorials 11 hours Coursework, further study and examination 67 hours Assessment 1 Class Test (1 hour) 10% TBC 1 Coursework 10% To be handed in to the School Coursework Office MB133 Examination (1.5 hours) 80% January Examination Feedback on the module will be given via a Class Test/Coursework Mark. All provisional marks will be available within 4 weeks. Feedback from the Class Test, Coursework and the Examination will take the form of a mark. In the case of the Class Test/coursework worked solutions will be provided. Module outcomes What the student should gain from successful completion of the module Knowledge and Understanding 1. Understand the underlying principles of probability and statistics. 2. Understand the key methods to analyse and present data. Intellectual Skills 1. Ability to recognise the situations in which techniques from probability and/or statistics are applicable. 2. Ability to select the correct method. 3. Ability to execute the method. Teaching/Learning Methods Assessment Methods Lectures/Tutorials Examination/ Coursework Lectures/Tutorials Examination/ Coursework SEAS, Aston University – AM Module Specification 2011/12 Last update 05/09/11 Professional/Subject-Specific Skills 1. Calculate the probability for events, using the elementary definitions of probability 2. Calculate (joint) expectation values for discrete and continuous random variables, determine their independence. 3. Summarise and present data in a meaningful way. 4. Calculate confidence limits for sampled data. 5. Perform tests of hypotheses concerning the mean, variance, goodness of fit and contingency tables. 6. Perform linear regression. Lectures/Tutorials Examination/ Coursework Lectures/Tutorials Examination/ Coursework Transferable Skills 1. Presentation, time management Reading List: Chatfield, C. (1995) Statistics for Technology. 3rd Edition Revised. CRC Press. Devore, J. (1995) Probability and Statistics for Engineering and the Sciences. 4th Edition. Wadsworth Publishing: California. (Accompanying software available at the Loans Counter). Lipschutz and Schiller (1998), Introduction to probability and statistics, Schaum’s outline series, McGraw-Hill. Stirzaker D. (1999), Probability and Random Variables: a Beginner's Guide, Cambridge UP. Walpole, R. E. Myers R.H. and Myers, S. L. (1998) Probability and Statistics for Engineers and Scientists. 6th Edition. Prentice and Hall: London. Co-requisites: Transition Mathematics (AM10TM) SEAS, Aston University – AM Module Specification 2011/12 Last update 05/09/11