Module code: G1100
15 credits in autumn semester
Teaching method: Lecture
Assessment modes: Unseen examination, Coursework
You cover topics including:
- short revision of probability theory
- expectation and conditional expectation
- convergence of random variables, in particular laws of large numbers, moment generating functions, and central limit theorem
- stochastic processes in discrete time in particular Markov chains, including random walk, martingales in discrete time, Doob's optional stopping theorem, and martingale convergence theorem.
Module learning outcomes
- Setting up probability spaces, events and random variables to solve real-life probability problems.
- Manipulating distributions, densities, sums of random variables, basic random processes and Markov chains with applications.
- Understanding and using the Laws of Large Numbers and the Central Limit Theorem, with an eye to statistics and probability modelling.
- Acquire and rediscover set-theoretical and calculus skills in the context of probabilistic manipulations.