# STU12501 – Introduction to Probability

**Source**: https://teaching.scss.tcd.ie/module/stu12501-introduction-to-statistics-i/
**Parent**: https://teaching.scss.tcd.ie/visiting-students/

|  |  |
| --- | --- |
| **Module Code** | STU12501 |
| **Module Name** | Introduction to Probability |
| **ECTS Weighting [**[1]**](https://teaching.scss.tcd.ie/wp-admin/post.php?post=375&action=edit#_ftn1)** | 5 ECTS |
| **Semester Taught** | Semester 1 |
| **Module Coordinator/s** | Fergal Shevlin |

## Module Learning Outcomes

1. Understand the elementary concepts of probability models.
2. Apply various probability models to practical problems in a range of disciplines.
3. Distinguish between discrete and continuous random variables.
4. Appreciate the elementary properties of random variables.

## Module Content

- **Sample Space and Probability:** Sets; Probabilistic Models; Conditional Probability; Total Probability Theorem and Bayes’ Rule; Independence; Counting.
- **Discrete Random Variables:** Probability Mass Functions; Functions of Random Variables; Expectation, Mean, and Variance; Joint PMFs of Multiple Random Variables; Conditioning; Independence.
- **General Random Variables:** Continuous Random Variables and PDFs; Cumulative Distribution Functions; Normal Random Variables.

## Teaching and Learning Methods

Lectures, homework, tutorials.

## Assessment Details

|  |  |  |  |  |  |
| --- | --- | --- | --- | --- | --- |
| **Assessment Component** | **Brief Description** | **Learning Outcomes Addressed** | **% of Total** | **Week Set** | **Week Due** |
| Examination | In-person examination (2 hours) | LO1,2,3,4. | 100% |  |  |

## Reassessment Details

In-person examination, 2 hours, 100%.

## Contact Hours and Indicative Student Workload

|  |  |
| --- | --- |
| **Contact Hours (scheduled hours per student over full module), broken down by**: | **33 hours** |
| Lectures (11 weeks x 2 hours.) | 22 hours |
| Laboratory | 0 hours |
| Tutorials (11 weeks x 1 hour.) | 11 hours |
| Other | 0 hours |
| **Independent study (outside scheduled contact hours), broken down by:** | **92 hours** |
| Suggested lecture preparation (11 weeks x 3 hours.) | 33 hours |
| Suggested homework problem-solving (11 weeks x 3 hours.) | 33 hours |
| Exam preparation (2 weeks x 13 hours.) | 26 hours |
| **Total Hours** | **125 hours** |

## Recommended Reading List

Extensive on-line course material associated with “Introduction to Probability”, 2nd Edition, Bertsekas and Tsitsiklis, Athena Scientific.

## Module Pre-requisites

None.

## Module Co-requisites

None.

## Module Website

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