# Statistics I

## Objectives

This unit allows the acquisition of competences related to the most the important techniques of description, summarization and exploration of data. Furthermore, it allows the acquisition of competences related to a set of concepts and methods of probability theory. The emphasis is especially on such topics which will be necessary for understanding statistical inference methods that are presented in other units. The aim is to deepen knowledge of descriptive statistics and probability theory, including the concepts of descriptive measures, conditional probabilities, independence, random variables and distribution functions, expectation, variance and moment generating function, joint probability distributions, and the most important probability distributions and their applications.At the end of this course, students should be able to:
- Organize information on charts and graphs
- Construct and interpret frequency tables
- Calculate and interpret descriptive measures
- Calculate probabilities by classical definition
- Calculate probabilities by the axiomatic and conditional probabilities definition
- Verify that two events are independent
- Determine and characterize the distribution function (df)
- Calculate probabilities based on the probability (density) function (pdf) and df
- Calculate the mean and variance and apply their properties
- Calculate the moment generating function and obtain the moments
- Indicate the characteristics of families of distributions and identify the distribution of concrete phenomena
- Calculate probabilities and percentiles of the Normal, Student-t, Chi-square, F
- Obtain joint probabilities, marginal distributions and conditional pdf
- Check if two random variables are independent
- Calculate the covariance and correlation coefficient
- Calculate joint probabilities and conditional probabilities of the bivariate Normal distribution

## General characterization

100053

6.0

##### Responsible teacher

Ana Cristina Marinho da Costa

##### Hours

Weekly - Available soon

Total - Available soon

##### Teaching language

Portuguese. If there are Erasmus students, classes will be taught in English

### Prerequisites

In order to meet the leaning objectives successfully, students must possess knowledge of Math I.

### Bibliography

• Pedrosa, A. C. e Gama, S. M. A. (2016). Introdução Computacional à Probabilidade e Estatística. 3ª edição, Porto Editora, reimpressão 07-2018.
• Afonso, A. e Nunes, C. (2011). Probabilidades e Estatística. Aplicações e Soluções em SPSS. Escolar Editora, Lisboa.
• Mood, A. M., Graybill, F. A. e Boes, D. C. (1974). Introduction to the Theory of Statistics.3rd Edition, McGraw?Hill.
• Murteira, B., Ribeiro, C. S., Silva, J. A. e Pimenta, C. (2002). Introdução à Estatística. McGraw Hill.
• Reis, E. (1996). Estatística Descritiva. 3ª Edição, Edições Sílabo, Lisboa.

### Teaching method

This course is mainly based on classes that are theoretical and practical, and there is a set of tutorial classes. The practical part of the course is aimed at solving problems and completing exercises. A series of exercises to be completed on an individual basis, outside classes, and during the tutorial classes is also made available.

### Evaluation method

1st call: three tests (35%, 20% and 45%, respectively). It is required a minimum of 8 points in the 3rd test for approval.
2nd call: final exam (100%).

## Subject matter

LU0. Descriptive statistics

• Introduction
• Organization of the information
• Frequency distributions
• Descriptive measures
LU1. Introduction to probability theory
• History
• Combinatorial models
• Probability definitions
LU2. Probability axioms
• Probability measure
• Conditional probability and independence
• Bayes’s theorem
LU3. Random variables and distribution functions
• Random variable concept
• Distribution function
• Discrete random variables
• Continuous random variables
LU4. Mathematical expectation and moments
• Mathematical expectation
• Variance
• Random variables’ moments
• Moment generating function
LU5. Specific probability distributions
• Uniform (discrete and continuous)
• Bernoulli
• Binomial
• Hypergeometric
• Negative Binomial
• Geometric
• Poisson
• Exponential
• Normal
• Chi-squared
• t-Student
• F-Fisher-Snedecor
LU6. Joint distributions
• Random vectors
• Bivariate discrete probability distributions
• Bivariate continuous probability distributions
• Bivariate Normal distribution

## Programs

Programs where the course is taught: