|Module Name||Applied Probability I|
|ECTS Weighting ||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 understand the concepts involved in simple and linear regression analysis Third learning outcome;
- To start learning R as programming language for Statistics/Probability.
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. Lecture and tutorial hours: 33, Lab hours: 5.
|Assessment Component||Brief Description||Learning Outcomes Addressed||% of Total||Week Set||Week Due|
|Final Exam||Real-Time Exam (2 hours)||All but LO7||80%||N/A||N/A|
|Project||Group Project||All||20%||Week 13||Week 18|
Written Exam, 100%.
Contact Hours and Indicative Student Workload
|Contact Hours (lectures, labs, tutorials, meetings, etc.)||38 hours|
|Independent Study (outside scheduled contact hours), broken down by:||32 hours|
|Preparation for classes and review of material (including preparation for examination, if applicable)||10 hours|
|Completion of assessments (including examination, if applicable)||22 hours|
|Total Hours||70 hours|
Recommended Reading List
- Tijms, “Understanding Probability”, Cambridge 2012.
- Additional material will be provided when needed.
Pre-requisite modules: CSU11001 and CSU11002 (or MA1E01 and MA1E02)
Other/alternative non-module prerequisites: N/A