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Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title Probability and Statistics
Module Code MS223
School School of Mathematical Sciences
Module Co-ordinatorSemester 1: Mingchuan Zhao
Semester 2: Ho Man Tai
Autumn: Ho Man Tai
Module TeachersGurpreet Singh
Thorsten Neuschel
Ho Man Tai
Mingchuan Zhao
NFQ level 8 Credit Rating 5
Pre-requisite None
Co-requisite None
Compatibles None
Incompatibles None
Repeat examination

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.

Workload Full-time hours per semester
Type Hours Description
Lecture24Two lectures per week
Directed learning2End of Semester Exam
Independent Study64Study over 16 weeks-including exam preiod
Tutorial10Weekly Tutorial
Directed learning25Solving Tutorial questions
Total Workload: 125

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

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

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.

Assessment Breakdown
Continuous Assessment20% Examination Weight80%
Course Work Breakdown
TypeDescription% of totalAssessment Date
In Class TestShort Test10%Once per semester
In Class TestShort Test10%Sem 2 End
Reassessment Requirement Type
Resit arrangements are explained by the following categories;
1 = A resit is available for all components of the module
2 = No resit is available for 100% continuous assessment module
3 = No resit is available for the continuous assessment component
This module is category 3
Indicative Reading List

  • J.J. Kinney: 2002, Statistics for Science and Engineering., AddisonWesley,
  • R.L. Finney and G. B. Thomas: 1994, Calculus, Addison Wesley,
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Date of Last Revision26-SEP-07

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