# 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 and marginal distributions

- 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

##### Code

100053

##### Credits

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*.3^{rd}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

The curricular unit is based on theoretical and practical lessons. A variety of instructional strategies will be applied, including lectures, slide show demonstrations, step-by-step applications, questions and answers. The sessions include presentation of concepts and methodologies, solving examples, discussion and interpretation of results. The practical component is geared towards solving problems and exercises, including discussion and interpretation of results. A set of exercises to be completed independently in extra-classroom context is also disclosed.

### 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

The curricular unit is organized in seven Learning Units (LU):

**LU0. ****Descriptive statistics**

- Introduction to statistics
- 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: