# STU23501 – Probability and Theoretical Statistics I

**Source**: https://teaching.scss.tcd.ie/module/stu23501-probability-and-theoretical-statistics-i/
**Parent**: https://www.maths.tcd.ie/undergraduate/modules/minor-stats.php

|  |  |
| --- | --- |
| **Module Code** | STU23501 |
| **Module Name** | Probability and Theoretical Statistics 1 |
| **ECTS Weighting****[**[1]**](#_ftn1)** | 5 ECTS |
| **Semester taught** | Semester 1 |
| **Module Coordinator/s** | Professor Simon Wilson |

## Module Learning Outcomes

On successful completion of this module, students will be able to:

\
LO1. Derive the probability space for simple experiments, and prove simple\
 properties of probabilities from its definition;\
LO2. Identify when random variables are independent, and derive conditional\
 distributions and expectations;\
LO3. Define the most common discrete and continuous random variables, and\
 compute their moments and probabilities, moment and characteristic\
 generating functions where appropriate;\
LO4. Define a multivariate distribution and calculate marginal and conditional\
 distributions from it;\
LO5. State and prove the laws of averages and of central limit;

## Module Content

This is a rigorous development of probability theory from an axiomatic foundation,\
along with some more advanced topics. The topics covered are:\
• Events and probabilities\
• The laws of probability\
• Independence and conditional probability\
• Discrete random variables\
• Continuous random variables\
• Multivariate distributions & independence\
• Moment and characteristic generating functions\
• The law of averages and the central limit theorem\
• Examples and past exam questions

## Teaching and learning Methods

Handouts and question sheets, as well as pre-recorded video lectures with accompanying lecture notes are available through Blackboard.

## Assessment Details

|  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- |
| **Assessment Component** | **Brief Description** | **Learning Outcomes Addressed** | **% of total** | **Week set** | Week Due |
| Examination | In person. To be completed in 2 hours | LO1, LO2, LO3, LO4, LO5 | 100 | n/a | n/a |

## Reassessment Details

In person examination (100%)

## Contact Hours and Indicative Student Workload

|  |  |
| --- | --- |
| **Contact Hours (scheduled hours per student over full module), broken down by**: | **33 hours** |
| Video lectures and reading notes | 33 hours |
| Laboratory | 0 hours |
| Tutorial or seminar | 24 hours |
| Other | 0 hours |
| **Independent study (outside scheduled contact hours), broken down by:** | **72 hours** |
| Preparation for classes and review of material (including preparation for examination, if applicable) | 41 hours |
| completion of assessments (including examination, if applicable) | 18 hours |
| **Total Hours** | **116 hours** |

## Recommended Reading List

Probability: an Introduction by Grimmett and Welsh, published by Oxford\
University Press.

\
Introduction to Probability Models by Ross, published by Academic Press (10th\
edition or later).

## Module Pre-requisites

**Prerequisite modules:** STU12501, STU12502

**Other/alternative non-module prerequisites:** e.g. programming languages,\
specified topics, etc.. This information will be particularly relevant for visiting\
students or students taking this module as an approved module (if applicable).

## Module Co-requisites

None

## Module Website

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