28171 - PROBABILITY II

Scheda insegnamento

Anno Accademico 2018/2019

Conoscenze e abilità da conseguire

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

Programma/Contenuti

  • 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

Testi/Bibliografia

  • 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

Metodi didattici

Regular lectures

Modalità di verifica dell'apprendimento

Written and oral exams

Strumenti a supporto della didattica

Notes provided at the beginning of the course

Orario di ricevimento

Consulta il sito web di Alberto Lanconelli