Taming Randomness: An Introduction to Probability Models

Chance plays an important part in all aspects of life.

We take chances every day: will a shot at goal land in the goal or miss? Will we be caught in a sudden shower or not? How long do we need to wait to be served in our favourite burger house?

Chance or random variation is also a central feature of all working systems: a scientist taking measurements in a lab; a disease spreading through a population; an economist studying price fluctuation. In all these processes some element of chance or randomness are present.  Is it possible to understand and therefore model and analyse such phenomena? If so, what are the tools we need to achieve that? Do we live in a world of randomness, or, as Einstein famously claimed, no one plays dice with the universe?

During this course, we will attempt to “tame randomness” using mathematics as our compass. 

Learning objectives:

• Develop a robust theoretical understanding of the basics of probability theory. 

• Develop the capability to identify the underlying randomness in real life problems, and decide how to model and quantify it.

• Gain an in-depth understanding of the basic technical tools needed in applied probability.

• Make use of random variables and theoretical probability distributions to model simple random processes (Η).