STU22004 – Applied Probability I

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.

Reassessment Details

Written Exam, 100%.

Contact Hours and Indicative Student Workload

• 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

N/A

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