Module: Probability 1

Module Specifications..

Current Academic Year 2023 - 2024

Please note that this information is subject to change.

Module Title	Probability 1
Module Code	MS117
School	School of Mathematical Sciences
Module Co-ordinator	Semester 1: Martin Venker Semester 2: Martin Venker Autumn: Martin Venker
Module Teachers	Martin Venker
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

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Array

Description

MS117 aims to introduce the basic concepts of probability theory through a mixture of lectures, demonstrations and assignments in R and problem solving based tutorials. The module will give students a working knowledge of the main techniques of elementary probability and build a solid foundation for learning more advanced topics in probability and statistics. Students must pass both the continuous assessment and end of semester exam for this module in order to pass the module.

Learning Outcomes

1. Define elementary concepts of probability and state the main theorems.
2. Use counting techniques to assign probabilities to events.
3. Compute and apply conditional probabilities
4. Derive the basic properties of common discrete and continuous distributions
5. Generate samples of random numbers from various distributions and investigate sample properties empirically in the R statistical computing language.
6. Derive the expectation and variance of important distributions and prove their theoretical properties

*Type*	*Hours*	*Description*
Workload	Full-time hours per semester
Lecture	24	Presentation of course material (including R demonstrations)
Tutorial	12	Working on solving tutorial and lab sheets.
Independent Study	89	Revising coursework, solving tutorials and completing assignments.
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

Revision of Probability Models and Combinatorics
Basic definitions and axioms, general probability models with discrete and continuous sample spaces. Basic rules, ordered samples unordered samples, partitions.

Conditional Probability
Independence, law of total probability, Bayes theorem.

Discrete Random Variables
Definition, probability functions, cumulative distribution function, expected values, variance, moments, medians and quartiles. Introduction to common discrete distributions.

Continuous Random Variables
Definition, probability density function, cumulative distribution function, expected values, variance, moments, medians and quartiles. Introduction to common continuous distributions.

Numerical Experiments in R
Inverse transform method, the central limit theorem, definition of a sample, numerical investigations of theoretical results in R.

Assessment Breakdown
Continuous Assessment	20%	Examination Weight	80%

Type	Description	% of total	Assessment Date
Course Work Breakdown
Assignment	Students will submit solutions to exercises.	20%	As required
Assignment	2 individual assignments in R applying techniques learned in lectures.	20%	As required

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

Geoffrey Grimmett and David Stirzaker: 2001, Probability and Random Processes, 3rd edition, Oxford University Press, Oxford,
Kai Lai Chung: 2003, Elementary Probability Theory with Stochastic Processes and an Introduction to Mathematical Finance, 4th edition, Springer, New York,
Richard Durrett: 1994, The Essentials of Probability, Duxbury Press, Belmont,
William Feller: 1971, An Introduction to Probability and its Applications, 3rd edition, Wiley, New York,
A. N. Shiryaev: 1996, Probability, 2nd edition, 1. chapter, Springer, New York,
Henk Tijms: 2007, Understanding Probability – Chance Rules in Everyday Life, 2nd edition, Cambridge University Press, Cambridge,
David Williams: 2001, Weighing the Odds – A Course in Probability and Statistics, Cambridge University Press, Cambridge,
Sheldon M. Ross: 2010, A first course in probability, 8th edition, Pearson, Englewood Cliffs,
Peter L. Bernstein: 1996, Against the Gods: The Remarkable Story of Risk, John Wiley & Sons, New York,

Other Resources

None

Programme or List of Programmes

ACM	BSc in Actuarial Mathematics
BPM	BSc in Psychology with Mathematics
CAFM	Common Entry, Actuarial, Financial Maths
DS	BSc in Data Science
SMPSC	Single Module Prof. Science and Health

Date of Last Revision

11-MAY-12

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