# 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]**](#_ftn1)** | 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:

1. Derive and implement confidence intervals and hypothesis tests for means and variances;
2. Conduct and explain the outputs of hypothesis testing in regression analysis;
3. Define and compute maximum likelihood estimates;
4. 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](https://projects.iq.harvard.edu/stat110/home)).
- 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

## Module Website

[Blackboard](https://tcd.blackboard.com/webapps/login/)