| Module Code | STU22004 |
| Module Name | Applied Probability I |
| ECTS Weighting [1] | 5 ECTS |
| Semester Taught | Semester 1 |
| Module Coordinator/s | Dr. James Ng |
Module Learning Outcomes
On successful completion of this module, students will be able to:
- To analyse problems by means of a Monte Carlo approach;
- To formalise and solve probability problems;
- To use the language of random variables, their expected values and their probability distributions;
- To use conditional distributions;
- To deal with special families of probability distribution;
- To start learning R as programming language for Statistics/Probability.
Module Content
Generation of random permutations:
- Frequentist probability;
- Axiomatic foundations of probability;
- Derivation of basic rules of probability from axioms;
- Independence of events;
- Conditional probability;
- Law of conditional probability, Bayes theorem;
- Random variables and their distributions;
- Expectation and its properties;
- Independent random variables;
- Transformations of random variables, Connection between distributions;
- Special families of discrete and continuous distributions;
- Markov inequality and Chebyschev inequality;
- Joint probability mass function, Marginal distributions;
- Covariance and correlation;
- Simple linear regression model;
- Monte Carlo approach;
- Empirical Law of Large Numbers;
- True and pseudo random number generation.
Teaching and Learning Methods
Lectures, laboratories and tutorials hours: 33.
Assessment Details
| Assessment Component | Brief Description | Learning Outcomes Addressed | % of Total | Week Set | Week Due |
| Final Exam | Real-Time Exam (2 hours) | All but LO6 | 80% | N/A | N/A |
| Project | Group Project | All | 20% | Week 13 | Week 18 |
Reassessment Details
Written Exam, 100%.
Contact Hours and Indicative Student Workload
| Contact Hours (lectures, labs, tutorials, meetings, etc.) | 33 hours |
| Independent Study (outside scheduled contact hours), broken down by: | 65 hours |
| Preparation for classes and review of material (including preparation for examination, if applicable) | 40 hours |
| Completion of assessments (including examination, if applicable) | 25 hours |
| Total Hours | 98 hours |
Recommended Reading List
- Tijms, “Understanding Probability”, Cambridge 2012.
- Additional material will be provided when needed.
Module Pre-requisites
Pre-requisite modules: CSU11001 and CSU11002 (or MA1E01 and MA1E02)
Other/alternative non-module prerequisites: N/A
Module Co-requisites
N/A