Module: Probability & Statistics

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Probability & Statistics
Module Code	CSC1028 (ITS: CA266)
Faculty	Engineering & Computing	School	Computing
NFQ level	8	Credit Rating	5

Description

Introduction to probability: discrete sample spaces; axioms; addition and multiplication laws; conditional probability and independence; reliability of systems; Bayes’ theorem. Discrete random variables and distributions: Bernoulli, hypergeometric, binomial, geometric and Poisson; expectation and variance; memoryless property; binomial approximation to the hypergeometric; Poisson approximation to the binomial. Continuous random variables and distributions: uniform, exponential and normal; expectation and variance; memoryless property of the exponential distribution. Modelling and simulation of stochastic systems, including small-scale computational simulations to approximate probabilities, validate analytic results, and estimate performance measures. Summarising and visualising statistical data using appropriate statistical computing tools.

Learning Outcomes

1. Explain and apply the axioms and fundamental laws of probability, including conditional probability, independence, and Bayes’ theorem.
2. Formulate and analyse discrete probabilistic models, including hypergeometric, binomial, geometric, and Poisson distributions; compute associated probabilities, expectations, and variances; and apply binomial and Poisson approximations where appropriate.
3. Formulate and analyse continuous probabilistic models, including the uniform, exponential, and normal distributions; compute associated probabilities, expectations, and variances.
4. Explain properties such as memorylessness where applicable.
5. Analyse simple reliability models involving independent component failures.
6. Model and simulate stochastic systems, using computational tools to approximate probabilities, validate analytical results, and estimate performance measures.
7. Use statistical computing tools (e.g., R) to summarise, analyse, and visualise data, including calculation of summary statistics and graphical representations.
8. Select and justify appropriate probabilistic models for problems arising in computing contexts.

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	2 lectures per week
Independent Study	89	post lecture study
Laboratory	12	Hands-on statistical computing and visualisation, small-scale simulations, and structured pen-and-paper probability exercises.
Total Workload: 125

Section Breakdown
CRN	10203	Part of Term	Semester 1
Coursework	20%	Examination Weight	80%
Grade Scale	40PASS	Pass Both Elements	N
Resit Category	RC1	Best Mark	N
Module Co-ordinator	Graham Healy	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	Lab exam 1	10%	n/a
In Class Test	Lab exam 2	10%	n/a
Formal Examination	End-of-Semester Final Examination	80%	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

Indicative Syllabus
Summarising and visualising statistical data using appropriate statistical computing tools; descriptive statistics; graphical representations. Discrete sample spaces; axioms of probability; addition and multiplication laws; conditional probability and independence; law of total probability; Bayes’ theorem; reliability of systems with independent components. Bernoulli, hypergeometric, binomial, geometric, exponential, and Poisson distributions; expectation and variance; memoryless property of the geometric distribution; binomial approximation to the hypergeometric; Poisson approximation to the binomial. Uniform, exponential, and normal distributions; expectation and variance; memoryless property of the exponential distribution. Basic simulation of stochastic systems; computational estimation of probabilities; validation of analytical results via simulation.

Indicative Reading List

Books:

Jane M. Horgan: 2009, Probability with R, Wiley, Hoboken, N.J., 978-0-470-28073-7
Dalgaard Peter: 2008, Statistics with R, 2nd,

Articles:
None

Other Resources

None