Module: Probability 1

Module Specifications.

Current Academic Year 2024 - 2025

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Date posted: September 2024

Module Title	Probability 1
Module Code	MS117 (ITS) / MTH1018 (Banner)
Faculty	Science & Health	School	Mathematical Sciences
Module Co-ordinator	Martin Venker
Module Teachers	-
NFQ level	6	Credit Rating	5
Pre-requisite	Not Available
Co-requisite	Not Available
Compatibles	Not Available
Incompatibles	Not Available

Repeat examination
This module is in resit category 3: no resit of the continuous assessment is available.

Description

MS117 aims to introduce the basic concepts of probability theory through a mixture of lectures and problem solving based tutorials. The module will give students a working knowledge of the main techniques of elementary probability and build a solid foundation for learning more advanced topics in probability and statistics.

Learning Outcomes

1. Define elementary concepts of probability and state the main theorems.
2. Use summation, integration, counting techniques and approximations to assign probabilities to events or compute distribution functions.
3. Compute and apply conditional probabilities.
4. Derive the basic properties of common discrete, continuous and mixed distributions.
5. Compute expectation, median and variance of given distributions and prove their theoretical properties.

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	36	Presentation of course material
Tutorial	24	Working on solving exercise sheets.
Independent Study	65	Revising coursework, solving tutorials and completing assignments.
Total Workload: 125

All module information is indicative and subject to change. For further information,students are advised to refer to the University's Marks and Standards and Programme Specific Regulations at: http://www.dcu.ie/registry/examinations/index.shtml

Indicative Content and Learning Activities

Principles of Modelling Chance
Probability spaces, construction of probability measures via densities, distribution functions

Conditional Probabilities and Independence
Conditional probabilities, law of total probability, Bayes theorem, independence

Standard Models In Probability
Combinatorics, random variables, common distributions in urn models: multinomial, binomial, (multivariate) hypergeometric, discrete and continuous waiting time distributions

Characteristics of Random Variables
Expectation, median, variance, standard deviation

Approximations of the Binomial Distribution
Poisson approximation, normal approximation

Assessment Breakdown
Continuous Assessment	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
In Class Test	n/a	20%	As required

Reassessment Requirement Type
Resit arrangements are explained by the following categories: Resit category 1: A resit is available for both* components of the module. Resit category 2: No resit is available for a 100% continuous assessment module. Resit category 3: No resit is available for the continuous assessment component where there is a continuous assessment and examination element.
* ‘Both’ is used in the context of the module having a Continuous Assessment/Examination split; where the module is 100% continuous assessment, there will also be a resit of the assessment
This module is category 3

Indicative Reading List

Hans-Otto Georgii: 2008, Stochastics, Walter de Gruyter, 9783110206760
Geoffrey Grimmett and David Stirzaker: 2001, Probability and Random Processes, 3rd edition, Oxford University Press, Oxford,
Kai Lai Chung: 2003, Elementary Probability Theory with Stochastic Processes and an Introduction to Mathematical Finance, 4th edition, Springer, New York,
Richard Durrett: 1994, The Essentials of Probability, Duxbury Press, Belmont,
William Feller: 1971, An Introduction to Probability and its Applications, 3rd edition, Wiley, New York,
A. N. Shiryaev: 1996, Probability, 2nd edition, 1. chapter, Springer, New York,
Henk Tijms: 2007, Understanding Probability – Chance Rules in Everyday Life, 2nd edition, Cambridge University Press, Cambridge,
David Williams: 2001, Weighing the Odds – A Course in Probability and Statistics, Cambridge University Press, Cambridge,
Sheldon M. Ross: 2010, A first course in probability, 8th edition, Pearson, Englewood Cliffs,
Peter L. Bernstein: 1996, Against the Gods: The Remarkable Story of Risk, John Wiley & Sons, New York,

Other Resources

None