Probability and Statistics
Faculdade de Ciências e Tecnologia
Departamento de Matemática
Teacher in charge
João Tiago Praça Nunes Mexia
Intuitive comprehension of the most important concepts of probabilities, such as: random variables; distributions; moments and Central Limit Theorem. It is stressed the importance of those mathematical tools in science and technology.
Comprehension of the classic statistical methods and concepts, such as; population and sample; estimators and pontual estimation; sampling distributions; confidence estimation; hypotheses testing; fit testing and regresion analysis.
Reasonable knowledge about real differentiation and integration.
Random experiment; Sample space; Random event; Algebra of events Axioms of probability e addition rules Conditional probability Total probability rule Bayes'''''''' theorem Random variable Discrete random variable Probability function Mean value and properties Variance, standard variation and properties Continuous random variable density function Distribution function Mean value, variance and standard deviation Chebychev inequality Discrete random pair Joint and marginal probability functions Covariance and properties Correlation coefficient and properties Important discrete distributions: Hipergeometric, Binomial, Poisson Important continuous distributions: Uniform, Exponencial, Weibull and Normal Central Limit Theorem
Elementar concepts in statistic Population, random sample and observed sample Simple random sample Pontual estimation Estimators and estimatives Desirable properties for estimators: Unbiased and minimum variance estimators Methods of point estimators: Method of moments Tests of hypotheses Elementar concepts Hypothesis, null hypothesis, alternative hypothesis, simple and compound hypotheses Decision and critical region Decision errors and probabilites Significance level and P-value Bilateral and unilateral tests for the: mean value, variance, standard deviation, proportion, fifference of mean values, ratio of variances Tests for validation on population conditions Randomeness test Testing for godness of fit to normality: chi-square test Confidence interval estimation: elementar concepts Confidence interval estimation for the: mean value, variance, standard deviation, proportion, fifference of mean values, ratio of variances Simple linear regression Pontual and confidence interval estimation for the model parameters Bilateral and unilateral tests for the model parameters Testing the quality of the model Pontual and confidence interval estimation on the: mean response and new observation prediction Contingency tables: test for independence
Montgomery, D.C.& Hines, W.W. (1990), Larson, H.J. (1969), Pestana, D.D. & Sílvio Filipe Velosa, S.F. (2002) Murteira, B.J.F. (1990), Robalo, A. (1994),
Montgomery, D.C.& Hines, W.W. (1990),
Larson, H.J. (1969),
Pestana, D.D. & Sílvio Filipe Velosa, S.F. (2002)
Murteira, B.J.F. (1990),
Robalo, A. (1994),
Lectures and problem-solving sessions, with wide participation of students and informatic software.
The evaluation is one of two: either the students take 2 tests or one exam. Each test covers half of the subjects taught, students must be classified over 7/20 in each test and they are approved in this subject if the average grade of the 2 tests is 10/20 or more or they get a grade of 10/20 or more in the exam. Students may have to do an oral examination to confirm a grade of more than 18/20.