STU22005 – Applied Probability II
Source: https://teaching.scss.tcd.ie/module/stu22005-applied-probability-ii/ Parent: https://www.maths.tcd.ie/undergraduate/modules/minor-stats.php
| Module Code | STU22005 |
| Module Name | Applied Probability II |
| ECTS Weighting [1] | 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.
Module Content
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 Details
| 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 |
| Continuous Assessment | Three live online quizzes run during the semester | All | 15% | Details on Blackboard | Details on Blackboard |
Reassessment Details
Examination (In-person 1.5 hours, 100%).
Contact Hours and Indicative Student Workload
| Contact Hours (scheduled hours per student over full module), broken down by: | 39 hours |
| Lecture and in-class discussion / question and answer sessions | 32 hours |
| Laboratory / Tutorial | 7 hours |
| Independent Study (outside scheduled contact hours), broken down by: | 86 hours |
| Preparation for classes and review of material (including preparation for examination, if applicable) | 81 hours |
| Completion of assessments (including examination, if applicable) | 5 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.
- Blitzstein JK, Hwang J. Introduction to Probability, Second Edition. CRC Press; 2019. doi:10.1201/9780429428357 (available in electronic form from the TCD library, and also has been made freely available by Harvard here: https://projects.iq.harvard.edu).
- Bain, L. J., & Engelhardt, M. (1992). Introduction to Probability and Mathematical Statistics. Brooks/Cole Cengage Learning.
- John A. Rice, Mathematical Statistics and Data Analysis, 3rd Edition
- Quinn, G. P., & Keough, M. J. (2002). Experimental design and data analysis for biologists. Cambridge university press.
Module Pre-requisites
*Prerequisite modules:* STU11002 and STU22004. Alternatively, STU12501, STU12502 and STU23501.
Module Co-requisites
N/A