STU22005 – Applied Probability II

Module CodeSTU22005
Module Name Applied Probability II
ECTS Weighting[1]5 ECTS
Semester taughtSemester 2
Module Coordinator/s  Prof. Caroline Brophy

Module Learning Outcomes

On successful completion of this module, students will be able to:
LO1. Derive confidence intervals and hypothesis tests for means and variances.
LO2. Derive prediction intervals for simple statistical models and explain
how they differ from confidence intervals.
LO3. Conduct and explain the outputs of hypothesis testing in regression
analysis.
LO4. Define maximum likelihood estimates and how to compute them.
LO5. Implement a bootstrap to construct confidence intervals.
LO6. Construct a q-q plot and use simple transformations of data that can
make it more Normally distributed.
LO7. Construct a probability plot for any given distribution where its
distribution function is known.
LO8. Calculate the properties of multivariate distributions.
LO9. Derive marginal and conditional probabilities of the bivariate Normal
distribution.

Module Content

Recap: derivation of the confidence interval and tests of hypothesis for normal data;
the difference between a confidence interval and a prediction interval.
The Central Limit Theorem and what it says about confidence intervals and tests of hypothesis.
Hypothesis testing for regression analysis.
The bootstrap approach to confidence intervals and tests of hypothesis.
Introduction to maximum likelihood estimation and computation.
The q-q plot and transforming data to make it more Gaussian.
Introduction to multivariate distributions.

Teaching and learning Methods

Lectures and laboratories.

Assessment Details

Assessment ComponentBrief Description Learning Outcomes Addressed% of totalWeek(s) setWeek(s) Due
Examination Real-time exam (2hrs)All85n/an/a
Continuous assessmentFour assessment sheetsAll (to date of each sheet)152, 4, 6, 83, 5, 7, 9

Reassessment Details

Examination (2 hours, 100%)

Contact Hours and Indicative Student Workload

Contact Hours (scheduled hours per student over full module), broken down by: 31 hours
Lecture22
hours
Laboratory9 hours
Tutorial or seminar0 hours
Other0 hours
Independent study (outside scheduled contact hours), broken down by:79 hours
Preparation for classes and review of material (including preparation for examination, if applicable)65 hours
Completion of assessments (including examination, if applicable)14 hours
Total Hours110 hours

Recommended Reading List

George Casella, Roger L. Berger, Statistical Inference, 2nd Edition

Douglas C. Montgomery, George C. Runger, Norma F. Hubele, Engineering Statistics,
5th Edition

Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining, Introduction to
Linear Regression Analysis, 5th Edition

Module Pre-requisites

Prerequisite modules: STU11002 and STU22004. Alternatively, STU12501, STU12502 and STU23501.

Module Co-requisites

N/A

Module Website

Blackboard