Background Course in Probability and Statistics (ECO-CO-PROB)
||ECO Compulsory courses
||0 (EUI Economics Department)
- Part-time Prof. C. Martinez Lafuente
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
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 1Topic 2
Expected values. Moments and moment generating functions. Transformations of
Casella and Berger, chapter 2Topic 3
Specific densities: discrete and continuous.
Casella and Berger, chapter 3Topic 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
Casella and Berger, chapter 4Topic 5
Large sample theory. Sums of random variables, convergence concepts. Laws of large
numbers. Central limit theorems. The delta method.
Casella and Berger, chapter 5Exercise classes
There will be 2 exercise classes.
Register for this course
Page last updated on 21 September 2018