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DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Probability with Applications (MATH08067)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Credit level (Normal year taken)SCQF Level 8 (Year 2 Undergraduate) AvailabilityAvailable to all students
SCQF Credits20 ECTS Credits10
SummaryThe 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Introduction to Linear Algebra (MATH08057) AND Calculus and its Applications (MATH08058)
Prohibited Combinations Students MUST NOT also be taking Probability (MATH08066) OR Statistics (Year 2) (MATH08051)
Other requirements None
Information for Visiting Students
Pre-requisitesVisiting students are advised to check that they have studied the material covered in the syllabus of each pre-requisite course before enrolling.
High Demand Course? Yes
Course Delivery Information
Academic year 2017/18, 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
Learning Outcomes
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.
Reading List
Students would be expected to own a copy of:

A First Course in Probability (8th Edition), Sheldon Ross. ISBN: 9781292024929 £52.99 from Blackwells.
Additional Information
Graduate Attributes and Skills Not entered
Course organiserDr Michal Branicki
Tel: (0131 6)50 4878
Course secretaryMr Martin Delaney
Tel: (0131 6)50 6427
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