Diacritica

The goal of the two courses (Probability theory I and II) is to give a rigorous and comprehensive introduction to Probability

The scope of the course:

- Measure-theoretic axioms of Probability
- Tools from measure theory: Dynkin's lemma, integration, Fubini, Kolmogorov extension theorem
- Sums of independent random variables: laws of large numbers, large deviation estimates, Kolmogorov's zero-one law
- Convergence of random variables
- Characteristic functions of random variables. The Central Limit Theorem
- Random walks: local CLT, recurrence and transience

Exam: Thursday, October 25, 10:15 - 13:00, D122 Exactum

Re-EXAMINATION DATES:
Tuesday 18.12.2018 10:00-13:00 Exactum B120;
Friday 11.01.2019 10:00-13:00 Exactum C123;
Thursday 4.04.2019 10:00-13:00 Exactum 122;
Wednesday 05.06.2019 10:00-13:00 Exactum B321;
Wednesday 14.08.2019 10:00-13:00 Exactum B321.

No registration required for those exams. You are welcome to try and improve your grade even if you have passed. There will also be one or two exams in summer.

Enrol

Messages

Konstantin Izyurov's picture

Konstantin Izyurov

Published, 25.4.2019 at 16:10

Dear course participants,

in the summer 2019, the course exam dates for both Probability theory I and II are:

Wednesday 05.06.2019 10:00-13:00 Exactum B321;
Wednesday 14.08.2019 10:00-13:00 Exactum B321.

No registration required for those exams. You are welcome to try and improve your grade even if you have passed. Apologies for spamming to those who are happy with their grades.

Kind regards,
Konstantin.

Konstantin Izyurov's picture

Konstantin Izyurov

Published, 14.12.2018 at 13:54

Dear course participants,

this message is for those who want to re-take Probability theory I exam, apologies to others for spam. The exam dates are:

Tuesday 18.12.2018 10:00-13:00 Exactum B120;
Friday 11.01.2019 10:00-13:00 Exactum C123;
Thursday 4.04.2019 10:00-13:00 Exactum 122.

No registration required for those exams. You are welcome to try and improve your grade even if you have passed. There will also be one or two exams in summer.

Kind regards,
Konstantin.

Konstantin Izyurov's picture

Konstantin Izyurov

Published, 21.11.2018 at 15:10

Dear course participants,

the next possibility to re-take the exam will be on Tuesday, December 18th, at B120, simultaneously with Probability theory II exam. You will have additional time in case you want to take both exams. Even if you passed the exam, you are welcome to try and improve you grade.

Sincerely,
Konstantin.

Konstantin Izyurov's picture

Konstantin Izyurov

Published, 10.9.2018 at 16:04

A few clarifications regarding the exercise bonus:

1) to obtain the exercise bonus, you should come to the exercises class. In the beginning of the class, you mark the exercises that you have solved. The teaching assistant (Joonas Turunen) will then check that you have really done them, either by asking a random person who marked the exercise as done to present the solution at the blackboard, or by arranging work in groups, or in some other way. You don't have to submit written solutions (unless instructed otherwise by Joonas).

2) if you do not attend the exercises class, you cannot obtain the bonus. Still, I strongly advise to at least seriously attempt to solve all the exercises, and then work through the model solutions of those exercises that you couldn't solve. This way, you learn enough to pass the exam with a good grade.

3) The exercise bonus is up to +2 points for the final grade, provided that your initial grade is >0. For example, if you have done all the exercises and your exam warrants grade 3, you get grade 5. If your exam warrants grade 0, you get 0 irrespective of the exercise bonus.

Kind regards,
Konstantin.

Timetable

Here is the course’s teaching schedule. Check the description for possible other schedules.

DateTimeLocation
Wed 5.9.2018
12:15 - 14:00
Thu 6.9.2018
10:15 - 12:00
Wed 12.9.2018
12:15 - 14:00
Thu 13.9.2018
10:15 - 12:00
Wed 19.9.2018
12:15 - 14:00
Thu 20.9.2018
10:15 - 12:00
Wed 26.9.2018
12:15 - 14:00
Thu 27.9.2018
10:15 - 12:00
Wed 3.10.2018
12:15 - 14:00
Thu 4.10.2018
10:15 - 12:00
Wed 10.10.2018
12:15 - 14:00
Thu 11.10.2018
10:15 - 12:00
Wed 17.10.2018
12:15 - 14:00
Thu 18.10.2018
10:15 - 12:00

Other teaching

04.09. - 16.10.2018 Tue 14.15-16.00
Konstantin Izyurov
Teaching language: English

Material

Lecture notes. You can get bonus points for pointing out mistakes in the lecture notes!

Tasks

Exericse set 1

Exercise set 2

Exercise set 2 - due on 18.09

Exercise set 3

Exercise set 3 - due on Tue 25.09

Exercise set 4

Due on 02.10

Exercise set 4

Exercise set 4 - due on Tue 9.10

Exercise set 6

Exericse set 6 - due 16.10

Description

Optional course.

Master's Programme in Mathematics and Statistics is responsible for the course.

The course belongs to the Mathematics and Applied mathematics module.

The course is available to students from other degree programmes.

Analysis I-II, Topology I, Vector analysis I, Measure and integral

Vector analysis II, Probability II.

The course gives a firm theoretical ground for Probability and introduces some of its classical results

Recommended time/stage of studies for completion: 1. year

Term/teaching period when the course will be offered: varying

Measure theoretic foundations of probability, independence, laws of large numbers, characteristic functions and the central limit theorm, Gaussian measures, recurrence/transience of random walks

Lecture notes; D. Williams: "Probability with martingales", R. Durrett: "Probability: theory and examples"

Lectures and exercise classes, possibly other methods like reading assignments+discussion

Exam and excercises, Course will be graded with grades 1-5

Exam, other methods will be described later