| CODE | SOR1510 | ||||||||||||
| TITLE | Foundations in Probability, Sampling and Estimation | ||||||||||||
| UM LEVEL | 01 - Year 1 in Modular Undergraduate Course | ||||||||||||
| MQF LEVEL | 5 | ||||||||||||
| ECTS CREDITS | 5 | ||||||||||||
| DEPARTMENT | Statistics and Operations Research | ||||||||||||
| DESCRIPTION | Elementary Probability: - Probability Axioms; - Combinatorial Probability; - Bayes鈥� Theorem. Random Variables: - Discrete and continuous random variables; - Discrete and Continuous Probability Distributions; - Expectation and Variance. Sampling Techniques: - Sampling Distributions and Confidence Intervals; - Means and Proportions; - Differences of Means and Proportions. Hypothesis testing: - Parametric tests and non-parametric tests for measures of central tendency; - Chi-squared test; - Correlation analysis. Monte Carlo Simulation: - Simulating from a distribution; - Monte Carlo integration for calculating expectations. Markov Chains: - Definition of Markov chains within the context of Stochastic Processes; - Transition probability matrices; - Chapman-Kolmogorov theorem; - Classification of states; - Asymptotic results for irreducible, recurrent, aperiodic Markov chains; - Stationary distributions; - Simulation and Monte Carlo; - Introduction to Continuous-time Markov chains. Study-Unit Aims: The aims of this study-unit are to: - Give the student the necessary probabilistic groundwork to solve problems in statistics and probability; - Provide the students with the skills of applying statistics to data and real-life scenarios; - Expose the student to different computational tools for the purposes of solving the above-mentioned statistical and probabilistic problems. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Give the student the necessary foundations in probability to understand statistical techniques; - Present the student with a wide variety of sampling and data collection methods; - Introduce the students the formulae required to obtain interval estimates related to means and proportions, and to calculate the needed sample size for a desired estimation accuracy; - Present the student with a repertoire of hypothesis tests to be used in different situations and for different types of data; - Introduce the students to Monte Carlo simulation, its use in simulating from distributions and calculating expectations; - Acquaint the student with Markov chains and their properties. 2. Skills: By the end of the study-unit the student will be able to: - Solve problems of intermediate complexity in probability and combinatorics; - Determine the appropriate sampling / data collection method to use in a variety of different contexts; - Obtain interval estimates related to means and proportions, calculate the needed sample size for a desired estimation accuracy, and perform the appropriate hypothesis tests for a number of given scenarios; - Use Monte Carlo simulation via statistical software to solve problems in probability; - Model situations and solve problems related to Markov chains; - Use software and develop programming skills to solve the computational problems described above. Main Text/s and any supplementary readings: Main Texts: - Asmussen, S. and Glynn P.W. (2007) Stochastic Simulation: Algorithms and Analysis, Springer New-York. - Jones, P.W. and Smith P. (2010) Stochastic Processes: An Introduction. Chapman&Hall. - Montgomery, D. and Runger, G. (2018) Applied Statistics and Probability for Engineers 鈥� Seventh Edition, Wiley. - Ross, S. M. (2014) Introduction to Probability & Statistics for Engineers 鈥� Fifth Edition, Academic Press. - Ross, S. M. (2005) Introductory Statistics 鈥� Second Edition, Academic Press. |
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| STUDY-UNIT TYPE | Lecture and Tutorial | ||||||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Mark A. Caruana Maria Kontorinaki David Paul Suda |
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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 2025/6. It may be subject to change in subsequent years. |
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