Module: Probability & Statistics

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Probability & Statistics
Module Code	MTH1080 (ITS: MS223)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	5

Description

The aim of this module is to give a thorough grounding in probability, statistics and calculus of several variables as required for the successful understanding and solution of problems in science. Students will learn how mathematics can be used as a tool for solving scientific problems and a language for communicating information. This is a know-how and skills module. Students will participate in the following learning activities: Lectures: Students will attend two one-hour lectures per week. These lectures are designed to introduce learners to the mathematical principles and problem solving techniques that underpin this module. Tutorials: Each student will attend one one-hour tutorial per week. Problem sheets based on lecture content are distributed to the students and they are strongly advised to attempt all tutorial questions in advance of the tutorial.Reading: Students are expected to fully utilise the textbooks recommended.

Learning Outcomes

1. apply the rules of probability and assign probabilities to events.
2. know how to obtain expectations of discrete and continuous random variables.
3. use the normal and student t-distributions to test statistical hypotheses and to compute confidence intervals.
4. perform the calculations that arise when the calculus of several variables is used to solve problems.

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	24	Two lectures per week
Directed learning	2	End of Semester Exam
Independent Study	64	Study over 16 weeks-including exam preiod
Tutorial	10	Weekly Tutorial
Directed learning	25	Solving Tutorial questions
Total Workload: 125

Section Breakdown
CRN	21076	Part of Term	Semester 2
Coursework	0%	Examination Weight	0%
Grade Scale	40PASS	Pass Both Elements	Y
Resit Category	RC3	Best Mark	Y
Module Co-ordinator	Natalie Behague	Module Teacher	Marco Viola

Type	Description	% of total	Assessment Date
Assessment Breakdown
In Class Test	Short Test	10%	Once per semester
In Class Test	Short Test	10%	Sem 2 End
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

Sets
Definitions, set operations; set identities. Russell's paradox.

Probability
Random experiments; axioms of probability; independent events; conditional probability; Bayes' theorem

Random variables and probability densities
Discrete and continuous random variables; characteristics of random variables; probability distributions and densities.

Some important probability densities
Basic combinatorics, the binomial, Poisson, Pascal and normal distributions.

Statistical inference
Point estimates and confidence intervals; the central limit theorem; hypothesis tests.

Vector calculus and functions of several variables
Vectors; scalar and cross product; applications. Scalar and vector fields; partial derivatives; div, grad and curl; surfaces; optimization problems.

Indicative Reading List

Books:

J.J. Kinney: 2002, Statistics for Science and Engineering., AddisonWesley,
R.L. Finney and G. B. Thomas: 1994, Calculus, Addison Wesley,

Articles:
None

Other Resources

None