MATH-432 / 5 crédits

Enseignant: Mountford Thomas

Langue: Anglais


Summary

The course is based on Durrett's text book Probability: Theory and Examples. It takes the measure theory approach to probability theory, wherein expectations are simply abstract integrals.

Content

(i) Definitions of probability space and random variables

(ii) independence

(iii) Different types of convergence for random variables.

(iv) Weak laws of large numbers

(v) Borel Cantelli Lemmas and Strong Law of large numbers

(vi) 0-1 laws

(vii) Convergence in law

(vi) Lindeberg-Feller CLT.

Keywords

sigma field

random variable

measurable

convergence a.s.

independence

Learning Prerequisites

Required courses

None but it helps to be familiar with measure threory.

Teaching methods

blackboard lectures

Assessment methods

Mostly the final exam but also exercises and a midterm

Resources

Moodle Link

Dans les plans d'études

  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Probability theory
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Type: optionnel
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Probability theory
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Type: optionnel
  • Semestre: Automne
  • Forme de l'examen: Ecrit (session d'hiver)
  • Matière examinée: Probability theory
  • Cours: 2 Heure(s) hebdo x 14 semaines
  • Exercices: 2 Heure(s) hebdo x 14 semaines
  • Type: optionnel

Semaine de référence

Mardi, 15h - 17h: Cours MAA112

Mardi, 17h - 19h: Exercice, TP MAA112

Cours connexes

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