|Module Name||Applied Probability II|
|ECTS Weighting ||5 ECTS|
|Semester Taught||Semester 2|
|Module Coordinator/s||Professor Caroline Brophy|
Module Learning Outcomes
On successful completion of this module, students will be able to:
- Derive and implement confidence intervals and hypothesis tests for means and variances;
- Conduct and explain the outputs of hypothesis testing in regression analysis;
- Define and compute maximum likelihood estimates;
- Implement a bootstrap analysis to construct confidence intervals and perform hypothesis tests.
This module will cover a range of topics, including:
- Recap of probability distributions;
- Derivation of the confidence interval and tests of hypothesis for normal data;
- The Central Limit Theorem and what it says about confidence intervals and tests of hypothesis;
- Hypothesis testing for regression analysis;
- The difference between a confidence interval and a prediction interval;
- The bootstrap approach to confidence intervals and tests of hypothesis;
- Introduction to maximum likelihood estimation and computation;
- Graphical assessments of normality;
- Introduction to multivariate distributions.
Teaching and Learning Methods
Lectures and laboratories.
|Assessment Component||Brief Description||Learning Outcomes Addressed||% of Total||Week Set||Week Due|
|Examination||In-person 1.5 hour exam||All||85%||N/A||N/A|
Examination (1.5 hours, 100%).
Contact Hours and Indicative Student Workload
|Contact Hours (scheduled hours per student over full module), broken down by:||42 hours|
|Lecture and in-class discussion / question and answer sessions||33 hours|
|Laboratory / Tutorial||9 hours|
|Independent Study (outside scheduled contact hours), broken down by:||83 hours|
|Preparation for classes and review of material (including preparation for examination, if applicable)||72 hours|
|Completion of assessments (including examination, if applicable)||11 hours|
|Total Hours||125 hours|
Recommended Reading List
- George Casella, Roger L. Berger, Statistical Inference, 2nd Edition.
- Douglas C. Montgomery, Elizabeth A. Peck, G. Geoffrey Vining, Introduction to Linear Regression Analysis, 5th Edition.
Prerequisite modules: STU11002 and STU22004. Alternatively, STU12501, STU12502 and STU23501.