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AM20PD Level: 5 PROBABILITY DISTRIBUTIONS Credits: 10 Teaching Period: 2 Module Tutors: Dr J Van Mourik Aims Understand the general principles of probability distributions. Be familiar with the properties of important probability distributions. Encounter some applications of probability distributions in random processes. Understand the Central Limit Theorem. They should be able to: Use probability distributions to calculate expectations. Determine marginal and conditional distributions and (in)dependence from joint probability distributions Use moment generating functions to derive properties of probability distributions. Apply the Central Limit Theorem. Analyse a simple random process. Content: Probability distributions for discrete and continuous random variables, including: Uniform, Bernoulli, Binomial, Poisson, Exponential, Normal, Gamma, Dirac Delta,... Joint probability distributions. Moment generating functions. The Central Limit Theorem and its applications Random processes. Teaching: Lectures 22 hours Tutorials 11 hours Coursework, further study and examination 67 hours Assessment: 1 Class Test (1 hour) 10% (week Date & Time TBC ) 1 Course Work 10% Examination (1.5 hours) 80% (Summer Examination) Module outcomes What the student should gain from successful completion of the module Knowledge and Understanding 1. Understand the underlying principles of probability and random variables. 2. Know the important properties of probability distributions. Intellectual Skills 1. Understand the underlying principles of probability and random variables. 2. Know the important properties of probability distributions. Professional/Subject-Specific Skills 1. Calculate expectation values for (joint) discrete and/or continuous random variables, determine their independence. 2. Derivation and use of the moment generating function for random variables. 3. Central Limit Theorem and its applications. 4. Application of properties of probability distributions to random processes. Transferable Skills 1. Presentation, time management SEAS, Aston University – AM Module Specification 2011/12 Teaching/Learnin g Methods Assessment Methods Lectures/Tutorials Examination/ Coursework Lectures/Tutorials Examination/ Coursework Lectures/Tutorials Examination/ Coursework Lectures/Tutorials Examination/ Coursework Last update 05/09/11 Reading List: Grimmet, G., Stirzaker, D. (1992) Probability and Random Processes. 2nd Edition. OUP: Oxford. 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. Prerequisites: Transition Mathematics (AM10TM) Statistics and Probability (AM10SP) Introduction to Analysis (AM10IA) Corequisites: Real Analysis (AM20RA) Multi-variate Calculus Analysis (AM20MC) SEAS, Aston University – AM Module Specification 2011/12 Last update 05/09/11