Module: Probability, Descriptive & Inferential Statis

Latest Module Specifications

Current Academic Year 2025 - 2026

Module Title	Probability, Descriptive & Inferential Statis
Module Code	MTH1048 (ITS: MS263)
Faculty	Mathematical Sciences	School	Science & Health
NFQ level	8	Credit Rating	7.5

Description

The aim of this module is to give a thorough grounding in probability, descriptive and inferential statistics, with an emphasis on the acquisition of both skills and understanding. Students will learn how probability and statistics can be used as a tool for solving problems and as a language for communicating information. Students will participate in the following learning activities: a) Lectures which are designed to introduce learners to the mathematical principles and problem solving techniques that underpin this module. b) Tutorials for which problem sheets based on lecture content will be distributed for the students to attempt in advance. c) Reading the textbooks recommended.

Learning Outcomes

1. Apply the rules of probability, assign probabilities to events, obtain expectations of discrete and continuous random variables.
2. Test statistical hypotheses and compute confidence intervals.
3. Demonstrate an understanding of concepts by use of examples or counterexamples.
4. Discuss the assumptions and limitations of conclusions drawn from sample data or graphical/numerical summaries of data

*Type*	*Hours*	*Description*
Workload	Full time hours per semester
Lecture	36	No Description
Tutorial	12	No Description
Independent Study	109	No Description
Directed learning	30	No Description
Total Workload: 187

Section Breakdown
CRN	20791	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	n/a	10%	As required
Assignment	n/a	10%	As required
Formal Examination	n/a	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.

Organising and Describing Data
Measures of central tendency and variability; graphical summaries.

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

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

Probability Density Functions
Basic combinatorics, the binomial, Poisson, Pascal and normal distributions.

Sampling
Random samples; sampling distribution; the central limit theorem; point estimation.

Hypothesis Testing
Confidence intervals; hypothesis tests.

Simple Linear Regression
Least squares; regression model; correlation.

Indicative Reading List

Books:

J.J. Kinney: 2002, Statistics for Science and Engineering, AddisonWesley,
J. I. BarraguÃ©s, A. Morais and J.Guisasola: 2014, Probability and Statistics : A Didactic Introduction, Taylor and Francis,

Articles:
None

Other Resources

None