Class Fundamentals of Statistics for Data Science

This curricular unit is devoted to fundamental concepts in the theory of probability and statistical inference.

1. Probability

Sample space; Events; Algebra of events and properties

Concepts of probability; Axiomatic of Kolmogorov;

Properties of probability function Conditional probability; Independence; Bayes theorem

2. Random Variables

Density functions Distribution function

Mean value, variance and standard deviation

3. Discrete distributions Binomial distribution Poisson distribution

4. Continuous distributions Normal distribution Exponential distribution

5. Statistical inference; Sampling distributions. Central limit theorem

6. Estimation. Confidence intervals for variance and proportion Tests of hypotheses

7. Linear Regression

Theorical concepts are introduced in class and then they are complemented with examples and exercises. For each topic, the students are given a set of exercises that aim to apply the theorical concepts. Exercises are discussed and solved in class, students are invited to share any doubts they might have. Continuous assessment of the students is obtained through seven short tests (20 minutes each); the average mark of these short tests will amount to 30% of the final grade.  The maximum between the grades of two exams  (90 minutes each) will amount to 70% of the final grade. Students are aproved with a final grade non smaller than ten (in a scale 0 to 20).

• Probabilidades e Estatística: Teoria, Exemplos & Exercícios: Manuel Cabral Morais 2020 IST Press (Coleção Ensino da Ciência e da Tecnologia)
• Introduction to Probability and Statistics for Engineers and Scientists : Ross, Sheldon M 2014 5th ed, Academic Press