Probabilidade 1

IMPA - March to June/2022

News

Lista em substituição do teste 2: clique aqui.
A prova 2 está remarcada para o dia 27/06/2022, das 9h às 12h, em sala a ser comunicada.
A prova 1 será no dia 28/04/2022, das 9h às 12h, na sala 349 do IMPA.
Check the dates for quizzes and exams below.

Informações gerais

Professor: Roberto Imbuzeiro Oliveira

Classes: Tuesdays and Thursdays from 9h to 10h30 in room 228

Course dynamics: This is an in-person class which may migrate to online depending on the surrounding circumstances. I will be speaking English, but students are welcome to also employ Portuguese and Spanish in class. All info in this page, including exam and test dates, is subject to change. It is highly recommended that all students make arrangements to be able to come to IMPA until the official end of the March - June 2022 term.

What is this class? Who is it for?

This is a class on Probability theory that assumes a strong background in Measure Theory and Integration. Like with all IMPA classes, anyone may register. The students who will benefit the most are those with a background compatible with the second year of our Masters. Topics to be covered include (but are not restricted to):

Kolmogorov's axioms for Probability theory and some measure theory results we will need.
Important distributions and some probabilistic models
Independent random variables and their sums: concentration and large deviations, weak and strong Laws of Large Numbers; Kolmogorov's results on 1, 2 and 3 series.
Weak convergence, characteristic functions and the central limit theorem for independent random variables.
Conditional expectation, conditional probabilities &c.
Constructions of probability measures in Polish spaces (including Komogorov's extension to countable products).
If time allows: Math Statistics (asymptotics for M-estimation); probabilistic method in Combinatorics; Brownian motion.

Bibliography and videos

The closest reference is Rick Durrett's, "Probability: Theory and Examples (5th edition)" . Augusto Teixeira's lecture notes are also a good reference. Louigi Addario-Berry's lecture notes will also be occasionally employed.

Other references: Richard Bass 's book is very clear, methodical and helpful.

Videos: A previous version of this class (also in English) by Claudio Landim is available from IMPA's Youtube channel.

Evaluation and grading

There will be two quizzes (testes) and two exams.

Testes will be 90 minutes long and will take place in class on April 7th. and June 9th. All three problems in each quiz/teste will come from the homework assignments.
Exams: these will take place on April 28th and June 27th 30th from 9h to 12h. Half the problems in each exam will come from homework.

Numerical and letter grades: the numerical grade is the maximum of MP and (2MP + MT)/3, where MP = average of exam grades and MT = average of exam grades. The final letter grade (A/B/C/F) will be (essentially) a function of the numerical grade, with a few bonuses.

Remark: all of the above is subject to change. It is highly recommended that all students make arrangements to be able to come to IMPA until the official end of the March - June 2022 term.