Background Course in Probability and Statistics (ECO-CO-PROB)
ECO-CO-PROB
Department |
ECO |
Course category |
ECO Compulsory courses |
Course type |
Course |
Academic year |
2023-2024 |
Term |
BLOCK 1 |
Credits |
0 (EUI Economics Department) |
Professors |
- Prof. C. Martinez Lafuente
|
Contact |
Simonsen, Sarah
|
Sessions |
31/08/2023 13:30-15:30 @ Seminar Room 3rd Floor,V. la Fonte
01/09/2023 15:00-17:00 @ Seminar Room 3rd Floor,V. la Fonte
05/09/2023 13:30-15:30 @ Seminar Room 3rd Floor,V. la Fonte
08/09/2023 16:00-18:00 @ Seminar Room 3rd Floor,V. la Fonte
11/09/2023 16:00-18:00 @ Seminar Room 3rd Floor,V. la Fonte
12/09/2023 16:00-18:00 @ Seminar Room 3rd Floor,V. la Fonte
15/09/2023 15:30-17:30 @ Seminar Room 3rd Floor,V. la Fonte
18/09/2023 16:00-18:00 @ Seminar Room 3rd Floor,V. la Fonte
19/09/2023 16:00-18:00 @ Seminar Room 3rd Floor,V. la Fonte
22/09/2023 15:30-17:30 @ Seminar Room 3rd Floor,V. la Fonte
|
Purpose
Cristina Lafuente Martinez (
[email protected])
The main goal of this core course is to give an introduction to the axiomatic foundations of probability theory and to the basics of univariate and bivariate statistics. The pre-course will consist of two parts of approximately equal size. The first part will focus on probability theory and will provide a mathematical structure for measures of uncertainty. In the second part the concept of random variables will be introduced and its properties will be discussed. Both parts will contain examples illustrating the basic concepts. There will be eight lectures and two exercise classes in this part.
Topics
Topic 1Introduction. Set theory. Basic probability theory. Probability axioms. Joint,
marginal and conditional probabilities. Random variables. Probability density and
cumulative distribution functions.
Casella and Berger, chapter 1
Topic 2Expected values. Moments and moment generating functions. Transformations of
random variables.
Casella and Berger, chapter 2
Topic 3Specific densities: discrete and continuous.
Casella and Berger, chapter 3
Topic 4Multivariate random variables. Joint and marginal distributions. Conditional distributions
and independence of random variables. Covariance and correlation. The
distribution of order statistics. Bivariate and multivariate normal densities. Conditional
normal densities. Bivariate transformations of random variables. Law of
Iterated Expectations.
Casella and Berger, chapter 4
Topic 5Large sample theory. Sums of random variables, convergence concepts. Laws of large
numbers. Central limit theorems. The delta method.
Casella and Berger, chapter 5
Exercise classesThere will be 2 exercise classes.
Description
See Syllabus
Register for this course
Page last updated on 05 September 2023