# DEGREE REGULATIONS & PROGRAMMES OF STUDY 2015/2016

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# Undergraduate Course: Probability with Applications (MATH08067)

 School School of Mathematics College College of Science and Engineering Credit level (Normal year taken) SCQF Level 8 (Year 2 Undergraduate) Availability Available to all students SCQF Credits 20 ECTS Credits 10 Summary The aim of this course is to develop the basic theory of probability, covering discrete and continuous topics as well as Markov chains and its various applications. The course will have four lecture theatre-hours per week, with the understanding that one of those or equivalent pro rata is for Example Classes and other reinforcement activities. Course description - Basic concepts, sample spaces, events, probabilities, counting/combinatorics, inclusion-exclusion principle; - Conditioning and independence, Baye¿s formula, law of total probability; - Discrete random variables (binomial, poisson, geometric, hypergeometric), expectation, variance, mean, independence; - Continuous random variables, distributions and densities (uniform, normal and exponential); - Jointly distributed random variables, joint distribution functions, independence and conditional distributions; - Covariance, correlation, conditional expectation, moment generating functions; - Inequalities (Markov, Chebyshev, Chernoff), law of large numbers (strong and weak), central limit theorem; - Discrete Markov chains, transition matrices, hitting times and absorption probabilities, recurrence and transience (of random walks), convergence to equilibrium, ergodic theorem; - Birth and death processes, steady states, application to telecom circuits, M/M/1 queque; - (Time permitting) Introduction to entropy, mutual information and coding.
 Pre-requisites Students MUST have passed: Introduction to Linear Algebra (MATH08057) AND Calculus and its Applications (MATH08058) Co-requisites Prohibited Combinations Students MUST NOT also be taking Probability (MATH08066) AND Statistics (Year 2) (MATH08051) Other requirements None
 Pre-requisites None High Demand Course? Yes
 Academic year 2015/16, Available to all students (SV1) Quota:  None Course Start Semester 2 Timetable Timetable Learning and Teaching activities (Further Info) Total Hours: 200 ( Lecture Hours 33, Seminar/Tutorial Hours 11, Summative Assessment Hours 3, Programme Level Learning and Teaching Hours 4, Directed Learning and Independent Learning Hours 149 ) Additional Information (Learning and Teaching) Students must pass exam and course overall. Assessment (Further Info) Written Exam 85 %, Coursework 15 %, Practical Exam 0 % Additional Information (Assessment) Coursework 15%, Examination 85% Feedback Not entered Exam Information Exam Diet Paper Name Hours & Minutes Main Exam Diet S2 (April/May) Probability with Applications (MATH08067) 3:00 Resit Exam Diet (August) Probability with Applications (MATH08067) 3:00
 1. Facility in practical calculations of probabilities in elementary problems. 2. To acquire a probabilistic understanding of various processes. 3. The ability to identify appropriate probability models and apply them to solve concrete problems. 4. Understanding basic concepts of and the ability to apply methods from discrete probability such as conditional probability and independence to diverse situations. 5. Understanding of and facility in the basic notions of continuous probability such as expectation and joint distributions. 6. To describe Markov chains and their use in a range of applications.
 Students would be expected to own a copy of: A First Course in Probability (8th Edition), Sheldon Ross. ISBN: 9781292024929 £52.99 from Blackwells.
 Graduate Attributes and Skills Not entered Keywords PwA
 Course organiser Prof Jim Wright Tel: (0131 6)50 8570 Email: J.R.Wright@ed.ac.uk Course secretary Mr Martin Delaney Tel: (0131 6)50 6427 Email: Martin.Delaney@ed.ac.uk
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