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

ECO-CO-PROB

Purpose

The main goal of this course is to review core concepts in probability theory and univariate and bivariate statistics. The pre-course will cover the building blocks of probability theory, moving to the study of random variables and their distributions (with a focus on the most important distributions for economists), basics of bivariate distributions, large sample theory and finish with an introduction to markov processes. All lectures will contain intuitive examples of basic concepts and practice problems.
There will be seven lectures and three exercise classes in this part.

 

Topics

 

Topic 1

Introduction. Set theory. Basic probability theory. Probability axioms. Joint, marginal and conditional probabilities.
Blitzstein and Hwang, chapters 1 and 2

Topic 2

Discrete random variables. Probability mass and cumulative distribution functions. Continuous Random Variables. Probability density functions. Important distribu- tions: Normal, Poisson, Exponential.
Blitzstein and Hwang, chapters 3 and 5

Topic 3

Expected values. Moments and moment generating functions. Transformations of random variables.
Blitzstein and Hwang, chapters 4, 6 and 8

Topic 4

Multivariate random variables. Joint and marginal distributions. Conditional dis- tributions and independence of random variables. Covariance and correlation. The distribution of order statistics. Bivariate and multivariate normal densities. Con- ditional normal densities. Bivariate transformations of random variables. Law of Iterated Expectations.
Blitzstein and Hwang, chapters 7 and 9

Topic 5

Large sample theory. Laws of large numbers. Central limit theorems. Markov Chains.
Blitzstein and Hwang, chapter 10 and 11


 

Exercise classes

There will be 3 exercise classes, one after topic 3, one after topic 5 and a final one covering problems from all topics.
 

Description

Teaching material

• Joseph K. Blitzstein and Jessica Hwang. Introduction to probability. Chapman and Hall/CRC, Second Edition, 2019.
• Lecture notes by the instructor, which will highlight the parts of the textbook that would be relevant for the course.

Other reference books:

• George Casella and Roger L. Berger. Statistical Inference. Thomson, Second Edition, 2002.
• Richard J. Larsen and Morris L. Marx. An introduction to mathematical statistics and its applications. Prentice Hall, Fifth Edition, 2012.

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