# STU12501 – Introduction to Statistics I (Probability)

## 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; Joint PDFs of Multiple Random Variables; Conditioning.
• Continuous Bayes’ Rule.

## Teaching and learning Methods

Lectures, homework, tutorials.

## Reassessment Details

Take-at-home examination, time-limited, 100%.

## Contact Hours and Indicative Student Workload

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

None.

None.

## Module Website

See TCD Blackboard.