Probabilities and Statistics

Objectives

Master concepts of statistical data analysis, probability theory and statistical inference to understanding and applying such concepts to solve real-life problems in engineering and science.

Program

- Graphical representation of static and dynamic statistical data with R.
- Basic concepts of probability theory. Conditional probability and total probability law. Bayes' theorem. Independence.
- Random variables (discrete and continuous). Distribution function. Probability mass function and probability density function. Expected value, variance and quantiles.
- Random pairs and linear transformation of random variables. Central limit theorem.
- Statistical inference. Point estimation and interval estimation.
- Hypothesis testing under normal populations.
- Goodness of fit testing.
- Linear regression.

Teaching Methodologies

The teaching methodologies aim to promote learning based on problem solving, reinforcing the practical component, activelearning, autonomous work and student accountability. The assessment model incorporates exam/tests, possibly with minimum grade, complemented with continuous evaluation components (70%) + computational projects (30%). Oral evaluation for grades above 17 (out of 20).

Bibliography

* Introduction to Probability and Statistics for Engineers and Scientists, Ross, Sheldon M, 2014, 5th ed, Academic Press;
* Probability and Statistics for Data Science: Math + R +, Matloff, N. , 2019, 1st ed., Data Chapman and Hall/CRC;
* Introductory Statistics with R, Dalgaard, P, 2002, Springer;
* A Modern Introduction to Probability and Statistics: Understanding Why and How, Dekking, F.M., Kraaikamp, C., Lopuhaä, H.P.,Meester, L.E., 2005, Springer.