MTH2225 Mathematics of uncertainty (Advanced)

When you finish this unit, you should be able to:

1. 1

   Model and interpret uncertainty using probability spaces, independence, conditional probability, and a range of discrete and continuous distributions, including multivariate contexts;

2. 2

   Analyse and compute expectations, variances, moments, and distributions, applying key results such as the Law of Large Numbers, Central Limit Theorem, and moment generating functions;

3. 3

   Apply simulation techniques and random number generation to approximate probabilities, expectations, and the behaviour of random processes;

4. 4

   Communicate probabilistic reasoning effectively and apply probability models to formulate and solve real-world problems in science, engineering, finance, and related disciplines;

5. 5

   Develop rigorous proofs of fundamental results in probability using advanced tools such as conditioning, generating functions, convergence concepts, and limit theorems.