| CODE | SOR1211 | ||||||||
| TITLE | Probability | ||||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 5 | ||||||||
| ECTS CREDITS | 2 | ||||||||
| DEPARTMENT | Statistics and Operations Research | ||||||||
| DESCRIPTION | Elementary Probability: - Sample space, events and probability of events - Mutually exclusive and independent events - Combinatorial Probability - Bayes’ Theorem Random Variables: - Discrete and continuous random variables - Expectation and Variance Discrete Probability Distributions: - Binomial Distribution - Poisson Distribution - Geometric Distribution Continuous Probability Distributions: - Exponential Distribution - Normal Distribution Study-unit Aims: The aims of this study-unit are to: - Discriminate between two selection methods (with and without replacement) and familiarize with different types of enumeration (multiplication rule, combinations and permutations); - Describe the properties of probability and use probability theory to solve problems for mutually exclusive events, independent events and conditional events; - Discriminate between discrete and continuous random variables and compute their expected value and variance; - Discriminate between different discrete distributions (Binomial, Poisson and Gemetric) and use these distributions to calculate the probabilities of discrete-type of random variables; - Discriminate between different continuous distributions (Exponential and Normal) and use these distributions to calculate the probabilities of continuous-type of random variables. Learning Outcomes: 1. Knowledge & Understanding By the end of the study-unit the student will be able to: - Understand the fundamental concepts of enumerative combinatorics (combinations and permutations) and analytic combinatorics (probability theory); - Familiarize with the concepts of expectation and variation and use these statistical tools to estimate the mean and variance of discrete and continuous random variables; - Discriminate between different types of discrete and continuous distributions and use these distributions to compute the probabilities of events. 2. Skills By the end of the study-unit the student will be able to: - Solve real life problems related to combinatorics and probability; - Identify the appropriate distribution of specific discrete and continuous variables and use the properties of these distributions to solve probability problems; - Use computer software, particularly EXCEL and R, to compute the probabilities of events for specific distributions, including the Binomial, Poisson, Geometric, Exponential and Normal distribution. Main Text/s and any supplementary readings: - Montgomery, D. and Runger, G. (2018) Applied Statistics and Probability for Engineers – Seventh Edition, Wiley. - Ross, S. M. (2014) Introduction to Probability & Statistics for Engineers – Fifth Edition, Academic Press. - Ross, Sheldon M. (2005) Introductory Statistics – Second Edition, Academic Press. |
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| ADDITIONAL NOTES | Pre-requisite Qualification: Pure or Applied Mathematics at the level requested for entry to Engineering and Technology courses. Statistics & O.R. study-units for students with 'A' Level Mathematics. This study-unit is not for students taking Statistics & O.R. as one of the principal subject area. |
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| STUDY-UNIT TYPE | Lectures, Tutorials & Computer Lab Sessions | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Louisa Testa Maria Kontorinaki |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years. |
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