# STU23501 – Probability and Theoretical Statistics I

## 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

Pre-recorded video lectures with accompanying lecture notes and handouts, available through Blackboard.  Question sheets will be handed out and answered in live sessions through Blackboard.

## Reassessment Details

Online examination, to be completed over 24 hours (100%)

## Contact Hours and Indicative Student Workload

University Press.

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).

None

Blackboard