Mathematics

Introduction to Probability

Module code: G5143
Level 5
15 credits in autumn semester
Teaching method: Lecture
Assessment modes: Coursework, Unseen examination

We begin exploring the notion of 'randomness' from a mathematical standpoint. We will harmonise normal experiences such as rolling dice, flipping coins, waiting in a queue, or answering randomly in a test with rigorous mathematical concepts, creating a synergy between applications, modelling and mathematical analysis.

We will begin with classical probability, developed since antiquity to model gambling questions and use the notion of conditional probability to resolve several `paradoxes’. Then we bring in the maths via the notion of a random variable and its distribution function. When we have these analytical concepts we define the expected value, variance, and other moments of a random variable, and develop the notion of independence. The final part of the module is limit theorems such as the law of large numbers and the central limit theorem.

Questions may include:

What is the probability to double your money in some casino games?
If you have tested positive for Covid, what is the probability you do not have it and the test is false? What if you did 2 tests?
What is the probability you wait at the bus stop for more than 10 minutes?
How are producers deciding their warranty length for expensive products?

Module learning outcomes

Select and employ appropriate methods to solve basic problems in probability;
Appreciate and understand common random variables;
Comprehend and use central theorems of Probability Theory.