Probability and Statistics D
It is objective of this subject to teach the basics about the theory of probability, namely about probability, conditional probability, independence, random variables - their distribution, moments and some other characteristics - and the central limit theorem.
The above matters are then used to teach the fundamentals about statistics, as the notion of population, sample and random sample, estimators, their sample distributions and some other properties, point estimation, estimation by confidence interval, hypotheses testing and simple linear regression.
The key important point here is one of teaching these subjects in a way that, in the future, students can: use adequately these probabilitiy and statistical tools, judiciously analyse statistical results and easily learn other statistical methods (not included in the discipline syllabous).
Maria de Fátima Varregoso Miguens
Weekly - 4
Total - 68
Basics of mathematical analysis, pointing out: some topological notions; analyses, diffrerential and integral knowledges about real (or R2) functions with one or more real variables.
Guimarães, R.C. e Cabral, J.S. (1997). Estatística, McGraw-Hill
Pedrosa, A. (2004). Introdução Computacional à Probabilidade e Estatística, Porto Editora
Murteira, B., Ribeiro, C.S., Silva, J.A. e Pimenta, C. (2002). Introdução à Estatística, McGraw-Hill
Montgomery e Runger (2002). Applied Statistics and Probability for Engineers. Wiley
Miguens, M.F.V. (2019). Textos de Apoio às disciplinas de serviço do DM. para a área de Probabilidades e Estatística. DMAT
Rohatgi (1976). An Introduction to Probability Theory and Mathematical Statistics. Wiley
Sokal e Rohlf (1995). Biometry. Freeman
Tiago de Oliveira (1990). Probabilidades e Estatística: Conceitos, Métodos e Aplicações, vol. I, II. McGraw-Hill
Paulino e Branco (2005). Exercícios de Probabilidade e Estatística. Escolar Editora
Robalo, A. (1994). Estatística Exercícios, Vol I, II. Edições Sílabo
Lectures and problem-solving sessions, with wide participation of students.
Frequency: Obtained with at least two thirds of attendance in classes taught in each module.
The students obtain approval if the weighted average of the three tests is greater than or equal to 9.5. If a student does not attend a test, this test will come with the factor of "0 x corresponding percentage" for the final classification.
Final mark = 40%T1 + 40%T2 + 20%T3
EVALUATION BY EXAM
The evaluation by exam is valid both for grade improvement as for discipline approval. The student with a final score greater than or equal to 17.5 should carry out an oral defense of note. Otherwise, will get a final score of 17.0.
More detailed rules are available in the Portuguese version
1. Basic notions of probability: Probability function and probability calculus of probabilities. Conditional probability (Bayes theorem) and independence of events
2. Discrete random variables (r.a.): Probability distributions and moments
3. Discrete random vectors: Joint and marginal distribution functions: Independence of v.a.''''''''s; Moments (correlation coefficient; Moments properties for linear tranformations of r.a.''''''''s
4. Continuous random variable: Density probability function, calculus of probabilities and moments
5 . Some important discrete distributions: Hipergeimetric, Bernoulli and Binomial, Poisson and his relation to Binomial, Poisson Process and Geometric.
6. Some important continuos distributions: Uniforme, Exponencial (and relations to Poisson Process), Normal (special emphasis) , t-Student and Qui-Square.
7. Central Limit Theorem
8. Basic notions of statistics, Random sample (r.a.) and stochastic properties for a resamplig extraction sample.
9. Pontual estimation: Desirable properties of no bias, efficiency and consistency
10. Interval estimation (Pivotal Method)
11. Hypothesis testing: Elementar concepts and their implementation for population parameters such as mean value, variance and porportion.
12. Simple linear regression and exemples for linearizable models.