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STAT7007 - Probability and Statistics

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Title:Probability and Statistics
Long Title:Probability and Statistics
Module Code:STAT7007
  
Duration:1 Semester
Credits: 5
NFQ Level:Intermediate
Field of Study: Mathematics
Valid From: Semester 1 - 2017/18 ( September 2017 )
Module Delivered in 4 programme(s)
Next Review Date: February 2022
Module Coordinator: David Goulding
Module Author: Robert Heffernan
Module Description: This module is an introduction to probability and statistical inference. Statistics deals with the organisation, presentation and interpretation of data and methods from the theory of probability are used as tools in statistical analysis. The emphasis will be practical and will be assisted by a statistical software package.
Learning Outcomes
On successful completion of this module the learner will be able to:
LO1 Apply probability axioms and rules including Bayes theorem.
LO2 Use software to graphically display and numerically summarise data.
LO3 Use probability distributions to model random variables.
LO4 Understand the need for sampling and calculate a regression line.
LO5 Calculate and interpret both confidence intervals and hypothesis tests for both means and proportions.
Pre-requisite learning
Module Recommendations

This is prior learning (or a practical skill) that is strongly recommended before enrolment in this module. You may enrol in this module if you have not acquired the recommended learning but you will have considerable difficulty in passing (i.e. achieving the learning outcomes of) the module. While the prior learning is expressed as named MTU module(s) it also allows for learning (in another module or modules) which is equivalent to the learning specified in the named module(s).
Incompatible Modules
These are modules which have learning outcomes that are too similar to the learning outcomes of this module. You may not earn additional credit for the same learning and therefore you may not enrol in this module if you have successfully completed any modules in the incompatible list.
No incompatible modules listed
Co-requisite Modules
More
No Co-requisite modules listed
Requirements

This is prior learning (or a practical skill) that is mandatory before enrolment in this module is allowed. You may not enrol on this module if you have not acquired the learning specified in this section.
No requirements listed
 

Module Content & Assessment

Indicative Content
Probability
Permutations and combinations. Classical, frequentist and axiomatic definitions. Laws of probability, independence, mutual exclusivity, conditional probability and Bayes' theorem. Tree diagrams.
Review of Descriptive Statistics
Presentation of data. Summary statistics. Histograms. Box plots. Use of software.
Probability Distributions
Random variables. Discrete vs Continuous. Expectation, mode, variance and standard deviation. Linearity of expectation. Binomial, Poisson and normal distributions. Use of software.
Sampling Theory
Sample statistics and sampling distributions. Central limit theorem. Confidence intervals for means and proportions. Determination of sample size. Hypothesis testing for small and large samples. Regression.
Assessment Breakdown%
Course Work30.00%
End of Module Formal Examination70.00%
Course Work
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Short Answer Questions In-class test: Probability, descriptive statistics and probability distributions. 1,3 15.0 Week 8
Practical/Skills Evaluation Practical Laboratory Examination 2,3,4 15.0 Week 12
End of Module Formal Examination
Assessment Type Assessment Description Outcome addressed % of total Assessment Date
Formal Exam End of Semester Final Examination 1,3,4,5 70.0 End-of-Semester
Reassessment Requirement
Repeat examination
Reassessment of this module will consist of a repeat examination. It is possible that there will also be a requirement to be reassessed in a coursework element.

The institute reserves the right to alter the nature and timings of assessment

 

Module Workload

Workload: Full Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Lecture Exposition of theory illustrated by concrete examples 3.0 Every Week 3.00
Tutorial Problem solving under the guidance of a tutor. 1.0 Every Second Week 0.50
Lab Practical with software package 1.0 Every Second Week 0.50
Independent Learning Completion of theory and practical exercises 3.0 Every Week 3.00
Total Hours 8.00
Total Weekly Learner Workload 7.00
Total Weekly Contact Hours 4.00
Workload: Part Time
Workload Type Workload Description Hours Frequency Average Weekly Learner Workload
Lecture Exposition of theory illustrated by concrete examples 1.5 Every Week 1.50
Tutorial Problem solving under the guidance of a tutor. 1.0 Every Second Week 0.50
Lab Practical with software package 1.0 Every Second Week 0.50
Independent Learning Completion of theory and practical exercises 5.0 Every Week 5.00
Total Hours 8.50
Total Weekly Learner Workload 7.50
Total Weekly Contact Hours 2.50
 

Module Resources

Recommended Book Resources
  • O'Shea, T. L. 2013, Essential Statistics for Researchers, IT Tralee [ISBN: 0957505906]
  • Kabacoff, R. 2015, R in Action, 2 Ed., Manning [ISBN: 9781617291388]
Supplementary Book Resources
  • Clarke G.M. and Cooke D. 1998, A Basic Course in Statistics,, 4 Ed., Arnold [ISBN: 0340719958]
  • Dalgaard, P 2002, Introductory Statistics with R, Springer [ISBN: 9780387954752]
This module does not have any article/paper resources
Other Resources
 

Module Delivered in

Programme Code Programme Semester Delivery
CR_KSDEV_8 Bachelor of Science (Honours) in Software Development 4 Mandatory
CR_KDNET_8 Bachelor of Science (Honours) in Computer Systems 4 Mandatory
CR_KCOMP_7 Bachelor of Science in Software Development 4 Mandatory
CR_KCOME_6 Higher Certificate in Science in Software Development 4 Mandatory

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