Mathematics

Introduction to Probability

Module code: G5211
Level 5
15 credits in autumn teaching
Teaching method: Workshop, Lecture
Assessment modes: Unseen examination, Coursework

This module will cover topics including:

  • elementary probability theory: axioms, probability measure, conditional probability, independence, Bayes formula and permutations and combinations
  • discrete distributions: expectation, variance, standard distributions, probability generating functions and sums of random variables and random walk
  • continuous distributions: densities, expectation, variance, standard distributions, transformations, linear function of independent normal random variables, normal approximations, central limit theorem, moment generating functions and law of large numbers
  • joint distributions: discrete and continuous, conditional distributions, covariance and correlation

Pre-requisite

none.

Module learning outcomes

  • Set up probability models for a range of random phenomena, both discrete and continuous;
  • Apply the notions of conditional probability;
  • Recognise where the use of certain standard probability distributions would be appropriate.