STU22004 – Applied Probability I

Module CodeSTU22004
Module NameApplied Probability I
ECTS Weighting [1]5 ECTS
Semester TaughtSemester 1
Module Coordinator/s  Dr. James Ng

Module Learning Outcomes

On successful completion of this module, students will be able to:

  1. To analyse problems by means of a Monte Carlo approach;
  2. To formalise and solve probability problems;
  3. To use the language of random variables, their expected values and their probability distributions;
  4. To use conditional distributions;
  5. To deal with special families of probability distribution;
  6. To understand the concepts involved in simple and linear regression analysis Third learning outcome;
  7. 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. Lecture and tutorial hours: 33, Lab hours: 5.

Assessment Details

Assessment ComponentBrief DescriptionLearning Outcomes Addressed% of TotalWeek SetWeek Due
Final ExamReal-Time Exam (2 hours)All but LO780%N/AN/A
ProjectGroup ProjectAll20%Week 13Week 18

Reassessment Details

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 Hours70 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

Module Website

Blackboard