STU22004 – Applied Probability I

Module CodeSTU22004
Module NameApplied Probability I
ECTS Weighting[1]5 ECTS
Semester taughtSemester 1
Module Coordinator/s  Dr. Bahman Honari

Module Learning Outcomes

On successful completion of this module, students will be able to:
LO 1. To analyse problems by means of a Monte Carlo approach
LO 2. To formalise and solve probability problems
LO 3. To use the language of random variables, their expected values and their
probability distributions
LO 4. To use conditional distributions
LO 5. To deal with special families of probability distribution
LO 6. To understand the concepts involved in simple and linear regression
analysis Third learning outcome
LO 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 (2hrs)All but LO 780N/AN/A
ProjectGroup projectAll201318




Reassessment Details

100% written exam

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 applicable10 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

Prerequisite modules: CSU11001 and CSU11002 (or MA1E01 and MA1E02)
Other/alternative non-module prerequisites: N/A

Module Co-requisites

None

Module Website

Blackboard