| Module Title |
Probability 1 |
| Module Code |
MTH1018 (ITS: MS117) |
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Faculty |
Science & Health |
School |
Mathematical Sciences |
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NFQ level |
8 |
Credit Rating |
5 |
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Description
Probability 1 aims to introduce the basic concepts of probability theory through lectures 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.
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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
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| Workload | Full time hours per semester | | Type | Hours | Description |
|---|
| Lecture | 36 | Presentation of course material. | | Tutorial | 12 | Working on solving tutorial sheets. | | Independent Study | 77 | Revising coursework, solving tutorials and exam preparation. |
| Total Workload: 125 |
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| Section Breakdown | | CRN | 20782 | Part of Term | Semester 2 | | Coursework | 20% | Examination Weight | 80% | | Grade Scale | 40PASS | Pass Both Elements | N | | Resit Category | RC3 | Best Mark | N | | Module Co-ordinator | Martin Venker | Module Teacher | |
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| Assessment Breakdown |
| Type | Description | % of total | Assessment Date |
|---|
| In Class Test | n/a | 20% | As required | | Formal Examination | End-of-Semester Final Examination | 60% | 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
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Pre-requisite |
None
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Co-requisite |
None |
| Compatibles |
None |
| Incompatibles |
None |
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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
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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.
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Indicative Reading List
Books:
- 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,
Articles:
None |
Other Resources
None |
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