Probabilidades e Estatística

The expository method is mainly used in theoretical classes, with the introduction of concepts and techniques, accompanied by examples associated with real data with application in the area of biomedical engineering. In theoretical-practical classes, students individually solve the exercises proposed by the teacher.
The Assessment may be carried out on a Distributed basis or by Final Exam. The distributed assessment consists of two tests, each lasting 1h30m and quoted at 10 points. The student can pass if the minimum grade in each of the tests is 4 values and the sum of the two grades is equal to or greater than 10 values. Assessment by Final Exam consists of an exam rated at 20 points, obtaining approval with a grade equal to or greater than 10 points.

Objectives: it is intended to transmit to students the fundamentals of Statistics necessary for the analysis and interpretation of data, especially in the area of health sciences, to present the main probability models with application in the fields of engineering.
Skills: learn the main methods of data interpretation and analysis and the probabilistic models that form the basis of statistical inference. Learn the basic tools of statistical inference, confidence intervals and hypothesis testing. Master the simple linear regression technique.

1. Introduction
2. Probability
2.1. Introduction
2.2. Random experience, results space, events
2.3. Definition of probability
2.4. Axioms and resulting theorems
2.5. Conditional probability
2.6. Independent events
2.7. Total probability theorem
2.8. Bayes theorem
3. Random variables and main theoretical distributions
3.1. Definition of random variable
3.2. Discrete random variables and continuous random variables
3.3. Probability function and probability density function
3.4. Distribution function
3.5. Location and dispersion parameters, properties
3.6. Special distributions: Binomial, Hypergeometric and Poisson, Continuous uniform, Exponen-tial and Normal
3.7. Brief reference to the Chi-Square distribution and t-Student distribution
3.8. Additivity of the Normal distribution
3.9. The central limit theorem
3.10. Discrete two-dimensional random variables: Definition
3.11. Joint probability and distribution functions
3.12. Marginal probability functions
3.13. Conditional probability functions
3.14. Independence of Random Variables
3.15. Covariance and Linear Correlation Coefficient
4. Sampling
4.1. Random sample
4.2. Sampling distributions.
5. Introduction to statistical inference
5.1. Point estimation: estimators and estimates
5.2. Properties of estimators
5.3. Range estimation
5.4. Basic notions
5.5. Confidence interval for the expected value of a normal population, with known or unknown variance
5.6. Confidence interval for the variance of a normal population
5.7. Fundamental notions about hypothesis testing
5.8. . Hypothesis testing for the expected value of a population
5.9. Hypothesis testing for the variance of a population
5.10. Hypothesis testing for the proportion of a population
6. Linear Regression
6.1. Linear regression
6.2. Scatter diagram
6.3. Minimum squares method
6.4. Regression line
6.5. Determination coefficient

NAO