Module: Probability 1

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Probability 1
Module Code	MTH1018 (ITS: MS117)
Faculty	Science & Health	School	Mathematical Sciences
NFQ level	8	Credit Rating	5

Description

Probability 1 aims to introduce the basic concepts of probability theory through 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

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2. Define elementary concepts of probability and state the main theorems.
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7. Use counting techniques to assign probabilities to events.
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12. Compute and apply conditional probabilities
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17. Derive the basic properties of common discrete and continuous distributions
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22. Generate samples of random numbers from various distributions and investigate sample properties empirically in the R statistical computing language.
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*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	36	Presentation of course material.
Tutorial	12	Working on solving tutorial sheets.
Independent Study	77	Revising coursework, solving tutorials and exam preparation.
Total Workload: 125

Section Breakdown
CRN	20782	Part of Term	Semester 2
Coursework	20%	Examination Weight	80%
Grade Scale	40PASS	Pass Both Elements	N
Resit Category	RC3	Best Mark	N
Module Co-ordinator	Martin Venker	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	n/a	20%	As required
Formal Examination	End-of-Semester Final Examination	60%	End-of-Semester

Reassessment Requirement Type
Resit arrangements are explained by the following categories; RC1: A resit is available for both^* components of the module. RC2: No resit is available for a 100% coursework module. RC3: No resit is available for the coursework component where there is a coursework and summative examination element. ^* ‘Both’ is used in the context of the module having a coursework/summative examination split; where the module is 100% coursework, there will also be a resit of the assessment

Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

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

Revision of Probability Models and Combinatorics
Basic definitions and axioms, general probability models with discrete and continuous sample spaces. Basic rules, ordered samples unordered samples, partitions.

Conditional Probability
Independence, law of total probability, Bayes theorem.

Discrete Random Variables
Definition, probability functions, cumulative distribution function, expected values, variance, moments, medians and quartiles. Introduction to common discrete distributions.

Continuous Random Variables
Definition, probability density function, cumulative distribution function, expected values, variance, moments, medians and quartiles. Introduction to common continuous distributions.

Indicative Reading List

Books:

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 â€“ Chance Rules in Everyday Life, 2nd edition, Cambridge University Press, Cambridge,
David Williams: 2001, Weighing the Odds â€“ 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,

Articles:
None

Other Resources

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