# Background Course in Probability and Statistics (ECO-CO-PROB)

## ECO-CO-PROB

 Department ECO Course category ECO Compulsory courses Course type Course Academic year 2021-2022 Term BLOCK 1 Credits 0 (EUI Economics Department) Professors Part-time Prof. C. Martinez Lafuente Contact Simonsen, Sarah Sessions

### 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

TBC

Page last updated on 21 September 2018