28171 - Probability II

Course Unit Page

Academic Year 2018/2019

Learning outcomes

By the end of the course the student should know the basic theory of multidimensional random variables and sequences of random variables. In particular the student should be able: - to derive the distribution of transformed random variables - to derive joint, conditional and marginal probability density functions - to state the definition and recall the properties of multivariate normal distributions – to investigate converge properties of sequences of random variables

Course contents

  • Review of basic probability
  • Characteristic function
  • Random vectors
  • Multinomial distribution
  • Multidimensional Gaussian distribution
  • Convergence concepts
  • Borel-Cantelli lemma
  • Law of large numbers
  • Convergence in distribution
  • Central limit theorem and applications

Readings/Bibliography

  • Kai Lai Chung, A course in Probability Theory - III edition, Academic Press, San Diego, 2001
  • Rick Durrett, Probability: Theory and Examples - IV edition, Cambridge University Press, Cambridge, 2013
  • John H. McColl, Multivariate probability, Arnold Publishers, London, 2004

Teaching methods

Regular lectures

Assessment methods

Written and oral exams

Teaching tools

Notes provided at the beginning of the course

Office hours

See the website of Alberto Lanconelli