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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 1
Introduction. 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 2
Expected values. Moments and moment generating functions. Transformations of
random variables.
Casella and Berger, chapter 2

Topic 3
Specific densities: discrete and continuous.
Casella and Berger, chapter 3

Topic 4
Multivariate 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 5
Large sample theory. Sums of random variables, convergence concepts. Laws of large
numbers. Central limit theorems. The delta method.
Casella and Berger, chapter 5

Exercise classes
There will be 2 exercise classes.

Description

See Syllabus

Page last updated on 05 September 2023