All students in the Statistics course are expected to have completed the Calculus I course. It is highly advisable that they have also completed the courses on Linear Algebra and Calculus II.

Once successfully having studied this subject, the students should be able to: - Analize problems involving random phenomena - Define populations for a statistical study - Build Hypothesis about a distribution - Estimate and test hypothesis about the paramters of the chosen model - Evaluate how well does the model fit to reality - Understand the limitations of the methods that have been studied and the conditions under which they lead to wrong conclusions

BLOCK I: PROBABILITY 1. Introduction to Probability 1.1 Introduction 1.2 Random phenomena 1.3 Definition of probability and properties 1.4 Conditional probability 1.5 Bayes Theorem 2. Random variables 2.1 Definition of random variable 2.2 Discrete random variables 2.3 Continuous random variables 2.4 Characteristic features of a random variable 2.5 Transformations of random variables 2.5 Random vectors 3. Distribution models 3.1 Binomial distribution 3.2 Poisson distribution 3.3 Uniform distribution (continuous) 3.4 Exponential distribution 3.5 Normal distribution (with CLT) 3.6 Multivariate normal distribution BLOCK II: STATISTICS 4. Parameter Estimation 4.1 Introduction and basic concepts 4.2 Sampling distributions 4.3 Maximum Likelihood Estimation 4.4 Properties of Maximum Likelihood Estimators 4.5 Inference based on MLEs 5. Statistical Inference 5.1 Introduction 5.2 Estimators and their distributions 5.3 Confidence Intervals 5.4 Hypothesis testing 5.5 Particualr tests on a single sample 5.6 Comparison of two populations BLOCK III: REGRESSION 6. Linear regression 6.1 Introduction 6.2 Simple linear regression 6.3 Multiple linear regression

- Lectures: introducing the theoretical concepts and developments with examples, 2.2 ECTS - Problem solving sessions: 2.2 ECTS - Computer (practical) sessions: 0.6 ECTS --- 4 SESSIONS - Evaluation sessions (continuous evaluation and final exam): 1 ECTS