Mathematics

Probability Models

Module code: G1100
Level 6
15 credits in autumn teaching
Teaching method: Lecture
Assessment modes: Coursework, Unseen examination

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.