In this curricular unit an introduction to Probability Theory and Statistical Inference, in its parametric version, is given.
The student should be able to do an exploratory data-analysis, apply correctly the probabilistic models studied and perform statistical analysis, specially when normal populations are involved.
0. Introduction to R software for statistical computing and graphics
1. Basic Concepts of Probability
1.1. Random experiment, outcomes, and events
1.2. Concept of Probability. The axioms of Kolmogorov. Relative frequency and subjective probability
1.3. Conditional Probability. Statistical Independence
1.4. Total probability and Bayes theorem
2. Random Variables and Multiple Random Variables
2.1. Discrete and continuous random variables
2.2. Cumulative distribution function. Probability mass function. Probability density function
2.3. Multiple random variables. Joint cumulative distribution function. Marginal and conditional distributions
2.4. Moments
3. Discrete and Continuous Probability Distributions
3.1. Discrete Distributions: Binomial, Hypergeometric and e Poisson
3.2. Continuous Distributions: Uniform, Exponential and Normal
3.3. Central limit theorem
4. Exploratory Data Analysis
4.1. Frequency distributions
4.2. Data summary
4.3. Data display
5. Distributions of sample statistics
5.1. Sampling distributions of sample mean and sample variance
5.2. Sampling distributions of sample proportions
6. Point Estimation and confidence interval estimation.
6.1. Point estimation
6.2. Confidence Intervals on the parameters of one or two Normal distributions.
6.3. Confidence Intervals for the population proportion
7. Hypotheses tests
7.1. Tests of hypotheses on the parameters of one Normal distribution
7.2. Tests of hypotheses for the population proportion
7.3. Tests of hypotheses on the parameters of two Normal distributions
7.4 Chi-Square goodness of fit test
7.5. Chi-Square independence test
8. Simple Linear Regression
8.1. Slope and intercept estimation
8.2. Inferences on the model's parameters
8.3. Adequacy of the regression model
Lectures - Consisting of exhibitions sections, where the fundamental concepts are presented using practical examples that illustrate the application of topic under study.
Practical Classes - articulated with the lectures, resorting to exposing and solving practical problems using the statistical software R.
The unit may also benefit from the use of the Moodle platform, where all materials to support course are available.
Baron, M. (2007). Probability and Statistics for Computer Scientists. Chapman & Hall/CRC, Boca Raton.
Dalgaard, P. (2002). Introductory Statistics with R. Springer, New York.
Guimarães, R.C., e Cabral, J.A.S. (1997). Estatística. McGraw-Hill, Lisboa.
Montgomery, D.C., and Runger, G.C. (2003). Applied Statistics and Probability for Engineers, 6ª ed., Wiley, New York.
Pestana, D.D. e Velosa, S.F. (2006). Introdução à Probabilidade e Estatística, Vol. I., 2ª ed., Fundação Calouste Gulbenkian, Lisboa.
Verzani, J. (2005). Using R for Introductory Statistics. Chapman & Hall/CRC, Boca Raton.
01060895
6