Full Title Applied Statistics and Probability

Short Title Applied Statistics and Probabi

Code MATH09004
Level 09
Credit 05

Author Creedon, Leo
Department Mech. and Electronic Eng.

Subject Area Mathematics
Attendence N/A%
Fee

Description

This module covers the statistics and probability required for a Masters in Engineering. The learner will gain the expertise to interpret the probabilistic models used in the engineering literature. It will cover statistical methods to analyse and quantify processes. It will enable learners to model problems using probabilistic and statistical mathematical methods.


Indicative Syllabus

Probability Theory

  • Random Variables
  • Probability Distributions
  • Marginal Probability
  • Conditional Probability
  • The Chain Rule of Conditional Probabilities
  • Independence and Conditional Independence
  • Expectation, Variance and Covariance
  • Common Probability Distributions
  • Useful Properties of Common Functions
  • Technical Details of Continuous Variables
  • Random Vectors

Estimation Theory

  • Estimators, Bias and Variance.

               MMSE, MAP, BLUE estimators

               Bias/Variance trade-off

  • Design of Experiments
  • Statistical Inference & Inferential thinking
  • Bayes’ Theorem
  • Maximum Likelihood
  • Stochastic Processes

Learning Outcomes
On completion of this module the learner will/should be able to
  1. Apply probability theory to analsye the centrality, dispersion and relationships within and between datasets and distributions. 

  2.  Apply experimental design and statistical inference to make inferences from data.

  3. Analyse the bias and variance of maximum likelihood and Bayesian estimators.

  4. Analyse stochastic processes (including Markov processes).

  5. Evaluate, select and apply appropriate statistical techniques to problems in the application field of study.

  6. Interpret the probability and statistics used in state of the art research publications and reproduce findings.

  7. Model an application specific problem with statistics and probability techniques.


Assessment Strategies

A terminal exam and continuous assessment will be used to assess the module.

To reinforce the theoretical principles covered in lectures, learners will participate in project work.

The learner will complete a final exam at the end of the semester.

The learner is required to pass both the continuous assessment and terminal examination element of this module.


Module Dependencies
Pre Requisite Modules
Co Requisite Modules
Incompatible Modules

Coursework Assessment Breakdown %
Course Work / Continuous Assessment 60 %
End of Semester / Year Formal Examination 40 %

Coursework Assessment Breakdown

Description Outcome Assessed % of Total Assessment Week
CA 1 1,2,3,4 30 Week 6
Project 1,2,3,4,5,6,7 30 Week 12


End Exam Assessment Breakdown

Description Outcome Assessed % of Total Assessment Week
Final Exam 1,2,3,4,5,6,7 40 End of Semester


Mode Workload

Type Location Description Hours Frequency Avg Weekly Workload
Lecture Lecture Theatre Lecture 2 Weekly 2.00
Laboratory Practical Computer Laboratory Laboratory Practical 2 Fortnightly 1.00
Independent Learning Not Specified Independent Learning 7 Weekly 7.00

Total Average Weekly Learner Workload 3.00 Hours

Mode Workload

Type Location Description Hours Frequency Avg Weekly Workload

Total Average Weekly Learner Workload 0.00 Hours

Mode Workload

Type Location Description Hours Frequency Avg Weekly Workload

Total Average Weekly Learner Workload 0.00 Hours

Mode Workload

Type Location Description Hours Frequency Avg Weekly Workload
Lecture Online Theory Lecture 1 Weekly 1.00
Independent Learning Not Specified Independent Learning 8.5 Weekly 8.50
Laboratory Practical Online Laboratory Practical 0.5 Weekly 0.50

Total Average Weekly Learner Workload 1.50 Hours

Resources
Book Resources

Other Resources

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Url Resources

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Additional Info

ISBN BookList

Book Cover Book Details
José Unpingco 2016 Python for Probability, Statistics, and Machine Learning Springer
ISBN-10 3319307150 ISBN-13 9783319307152
Christopher M. Bishop 2007 Pattern Recognition and Machine Learning (Information Science and Statistics) Springer
ISBN-10 0387310738 ISBN-13 9780387310732