Base Knowledge
Recommended Knowledge
Differential and integral calculus.
Teaching Methodologies
Teaching Methods
Theoretical classes will use the expository method.
Practical classes will be dedicated to problem solving, under the guidance of the teacher
Learning Results
Goals
It is intended that students acquire basic concepts of statistics and probability, including the language and rules inherent to those concepts, and relate the learned language/concepts to real everyday problems.
Skills
It is intended that the student has the skills to identify techniques that allow the statistical analysis of data and perform, if necessary, statistical inference, possibly resorting to statistical software.
Program
Syllabus
1. Probability
Random experiences. Results space. Events. Event space. Notions of probability. Resulting axioms and theorems. Conditioned probability. Independent events. Total probability Theorem and Bayes’ Theorem.
2. Discrete Random Variables and Discrete Probability Distributions
Definition of random variable. Discrete random variable. Probability finction and distributin function. Expected value, variance and properties. Hypergeometric distribution, Binomial distribution, Geometric distribution and Poisson distribution. Discrete bidimensional random variables. Joint probability function and joint distribution function. Marginal probability functions. Conditioned probability function. Independent random variables. Covariance and correlation coefficient.
3. Continuous Random Variables and Continuous Probability Distributions
Continuous random variables. Probability density function and distribution function. Expected value, variance and properties. Continuous uniform distribution. Normal distribution. Exponential distribution. Central Limit theorem and applications.
4. Sampling. Samplig distributions. Estimation
Introduction to statistical inference. Random sampling. Point estimation. Estimators and estimates. Estimator properties. Interval estimation. Confidence interval for the expected value of a normal population. Confidence interval for the variance of a normal distribution. Confidence interval for the difference of expected values and for the quotient of variances of two normal distributions.
5. Parametric hypothesis tests.
Introduction, notions and methodology. Testing the expected value. Testing the variance of a normal distribution. Testing the proportion. Testing the difference of expected values and the quotient of variances of normal distributions.
If possible, a brief introduction to software for statistical data analysis will be presented, with applications to the syllabus decribed above.
Curricular Unit Teachers
Internship(s)
NAO
Bibliography
Bibliography
Recommended:
Notes for theoretical classes, provided by the teacher
Pedrosa A., Gama S. (2004) Introdução Computacional à Probabilidade e Estatística, Porto Editora
Guimarães R., Cabral J. (2007) Estatística, 2 ed., Mc Graw Hill
Complementary:
Bowker A, Lieberman G. (1972) Engineering Statistics, 2 ed., Prentice Hall
Murteira B. et all (2002) Introdução à Estatística, Mc Graw-Hill
Ross S. (2004) Introduction to Probability and Statistics for Engineers and Scientists, 3 ed., Elsevier