In semester 5, we looked at a number of problems involving basic probability. In this module we will build on this and look at problems requiring more advanced treatment, in particular, the use of discrete and continuous probability distributions.

Marko chains are models where the system can be in any one of distinct states and we have known, fixed probabilities of transiting between various pairs of states.

Cellular automaton models are discrete, rule-based systems where simple local interactions between cells on a grid generate complex global patterns and behaviors over time.

Agent-based modeling (ABM) is a way of simulating complex systems by creating virtual 'agents', which are individual entities that follow simple rules and interact with each other and their environment. Each agent acts independently, making decisions based on its surroundings and goals, much like how people, animals, or even businesses behave in real life.