UC3M · Master CReMa and ME · 2026–27

Introduction to
Probability & Statistics

A rigorous foundations course for the Master in Competition Economics, Regulation and Markets and the Master in Economics at Universidad Carlos III de Madrid.

September 2026
Online Course
100% English
Access Course Materials

Course Outline

Here you can find a general outline of the course. The idea is to follow it in order, since most of the chapters build on the previous ones.

UnitTopicMaterials
1Probability Foundations→ Unit 1
2Random Variables & Univariate Distributions→ Unit 2
3Joint, Marginal & Conditional Distributions→ Unit 3
4Expectation, Variance & Higher Moments→ Unit 4
5Covariance, Conditional Expectation & Random Vectors→ Unit 5
6Special Distributions incl. Multivariate Normal→ Unit 6
7Law of Large Numbers & Central Limit Theorem→ Unit 7
8Point Estimation: MLE & OLS→ Unit 8
9Confidence Intervals & Hypothesis Testing→ Unit 9
10Final Exam: The exam questions will be based on the questions at the end of each set of lecture notes.

Lecture Notes & Slides

Below, you can find the lecture notes for each unit. If you have any questions, or if you find any typos in the notes or slides, please feel free to reach out to me. To access to the material you have to access through your uc3m email.

Unit 1
Probability Foundations
Sample spaces, events, axioms of probability, counting rules, conditional probability and independence.
Unit 2
Random Variables & Univariate Distributions
Bayes' theorem, random variables, probability mass and density functions, the c.d.f.
Unit 3
Joint, Marginal & Conditional Distributions
Two random variables: joint p.m.f./p.d.f., marginals, independence, and conditional distributions.
Unit 4
Expectation, Variance & Higher Moments
Mean and median, linearity, Jensen's inequality, variance, standard deviation, skewness and kurtosis.
Unit 5
Covariance, Conditional Expectation & Random Vectors
Covariance, correlation, the conditional expectation function (CEF), and extension to random vectors.
Unit 6
Special Distributions incl. Multivariate Normal
Bernoulli, Binomial, Poisson, Uniform, Exponential, Normal, χ², t, F, and the multivariate normal.
Unit 7
Law of Large Numbers & Central Limit Theorem
Convergence concepts, weak and strong LLN, the CLT and its applications, the Delta method.
Unit 8
Point Estimation: MLE & OLS
Estimators and their sampling distribution; bias, consistency, efficiency; the simple linear regression model and OLS.
Unit 9
Confidence Intervals & Hypothesis Testing
CIs, hypothesis tests, p-values, and inference on the OLS slope.
JF
Javier Fuertes-Pina
PhD Candidate · UC3M

About the Instructor

I am a PhD candidate in the Department of Economics at Universidad Carlos III de Madrid. My research focuses on nonparametric econometrics, demand estimation, and Discrete Choice Models, with a particular interest in semiparametric approaches and machine learning methods for empirical economics.

In this introductory course I aim to build solid probabilistic and statistical foundations that will support the more advanced quantitative methods you will encounter throughout your first course in Econometrics.

Do not hesitate to reach out with questions, comments, or requests for additional material. My contact details are in the section below.

Questions & Comments

Feel free to reach out with any questions about the course material, problem sets, or general queries. I am happy to help.

Department of Economics · UC3M · Campus Getafe

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