Module: Probability & Statistics

Latest Module Specifications

Current Academic Year 2025 - 2026

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

Description

Summary: Summarising and displaying statistical data in R; Introduction to probability: discrete sample spaces; axioms; addition and multiplication laws; conditional probability and independence; reliability of systems; Bayes theorem; • Discrete Random Variables: Bernouilli, hypergeometric, binomial, geometric and Poisson distributions; expectation; Sampling Inspection Schemes: Single and double sampling; operating characteristic function; average outgoing quality; consumers's and producer's risks. Continuous Random Variables: Uniform, exponential and normal distributions; normal approximation to binomial. Tchebechev's and Markov's inequalities • Aims: • To introduce the basic probability concepts and their applications to computer disciples; • To provide an understanding of discrete and continuous distributions; • To cover the essentials of the statistical computing system R. • To introduce the essentials of statistical analysis using R

Learning Outcomes

1. At the end of the module the student will: • have a through understanding of the statistical computing system R; • understanding the basics of probability; • recognise problems that may be solved using the standard discrete and continuous statistical models; • know how to obtain expectations of discrete and continuous random variables; • have developed a package in R to generate pdfs and cdfs of discrete distributions • be able to carry out a basic statistical analysis in R, including measures of central tendency and dispersion, and graphical displays such as stem and leaf, and boxplots.

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	2 lectures per week
Tutorial	12	1
Independent Study	48	post lecture study
Group work	30	project development
Laboratory	12	learning R
Total Workload: 126

Section Breakdown
CRN	10203	Part of Term	Semester 1
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC1	Best Mark	N
Module Co-ordinator	Graham Healy	Module Teacher

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	R lab exam	20%	Week 10
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 displaying statistical data in R; Introduction to probability: discrete sample spaces; axioms; addition and multiplication laws; conditional probability and independence; reliability of systems; Bayes theorem; • Discrete Random Variables: Bernouilli, hypergeometric, binomial, geometric and Poisson distributions; expectation; Sampling Inspection Schemes: Single and double sampling; operating characteristic function; average outgoing quality; consumers's and producer's risks. Continuous Random Variables: Uniform, exponential and normal distributions; normal approximation to binomial. Tchebechev's and Markov's inequalities •

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