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Module Specifications

Current Academic Year 2012 - 2013
Please note that this information is subject to change.

Module Title	Probability 1
Module Code	MS117
School	School of Mathematics
Online Module Resources
Module Co-ordinator	Semester 1: Olaf Menkens Semester 2: Olaf Menkens Autumn: Olaf Menkens
NFQ level	8	Credit Rating	5
Pre-requisite	None
Co-requisite	None
Compatibles	None
Incompatibles	None

Description

Module Aims:To introduce the basic concepts of Probability Theory using gambling problems as motivating examples.To give the students a working knowledge of the main techniques of elementary probability.

Learning Outcomes

1. Define elementary concepts of probability and state 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

Workload	Full-time hours per semester
*Type*	*Hours*	*Description*
Lecture	24	Lecture
Tutorial	12	Tutorial
Independent learning time	89	No Description
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

Probability Models.
basic definitions and rules, examples, general probability model with discrete and continuous sample spaces.[CT3--(ii)].

Elements of Combinatorial Analysis.
basic rules, ordered samples, unordered samples, partitions..

Conditional Probability.
independence, formula of total probability, Bayes formula.[CT3 (ii)].

Independent Trials.
Bernoulli trials, binomial distribution, negative binomial distribution, multinomial distribution, hypergeometric distribution. [CT3--(v)].

Discrete Random Variables.
joint distributions, conditional distributions, distribution of thesums of two random variables, expectations, variance.[CT3--(iii),(v)].

Moments.
Probability generating functions. Applications to determining densities of sums of discrete random variables, Binomial, Poisson, Geometric. Chebyshev's Inequality[CT3--(iv)].

Continuous Random Variables.
uniform distribution, exponential distribution, Cauchydistribution, Gaussian (or normal) distribution, probability density function. [CT3--(iii),(v)].

Assessment Breakdown
Continuous Assessment	25%	Examination Weight	75%

Course Work Breakdown
Type	Description	% of total	Assessment Date
Presentation	Presenting solutions of tutorial questions at the blackboard and answer questions on it.	25%	As required

Reassessment Requirement
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,