# Probability Theory and Statistics

Course Code : | 1002WETKST |

Study domain: | Mathematics |

Academic year: | 2017-2018 |

Semester: | 1st semester |

Sequentiality: | Credit for Mathematical methods for physics I & II. |

Contact hours: | 60 |

Credits: | 6 |

Study load (hours): | 168 |

Contract restrictions: | No contract restriction |

Language of instruction: | Dutch |

Exam period: | exam in the 1st semester |

Lecturer(s) | Sandra Van Aert |

### 1. Prerequisites *

- competences corresponding the final attainment level of secondary school

an active knowledge of

- Dutch

- general knowledge of the use of a PC and the Internet

specific prerequisites for this course

No previous knowledge of statistics is required. The course requires a basic knowledge of mathematical analysis: convergence, limits, derivatives, integrals. Familiarity with a PC and basic knowledge of simple programming algorithms.

### 2. Learning outcomes *

- The student will be able to justify, explain and apply statistical methods with respect to concrete research questions.
- The student acquires an understanding of statistical methods.
- The student can make an appropriate choice between the different existing statistical methods.
- The student is able to construct an accurate reasoning (from analysis to solution and conclusion).
- The student can use the software Matlab.
- The student acquires a basic understanding of relevant scientific methods and techniques, develops in problem-solving skills, can synthesise and integrate different perceptions, and learns to apply and assess methods in a critical way.

### 3. Course contents *

The purpose of statistics is to summarize a large amount of data and from this to retrieve useful information.In the course Probability Calculus and Statistics, the theoretical foundations and appropriate statistical methods to reach this goal are discussed. The theoretical part of the course is illustrated by means of a wide range of scientific and technological applications. The practical exercises are given separately. Herethe focus is on the application of statistical methods to a broad range of experimental data.

At the beginning of the course you will get an overview of graphical and numerical representations to summarize data. Then concepts of probability theory are explained and the most important probability distributions introduced. Then we will discuss the methodology to construct confidence intervals and to test statistical hypotheses. Finally, statistical parameter estimation is discussed.

The course-content has the following chapters:

- General introduction : purpose of statistics
- Descriptive statistics : graphical and numerical representation to summarize the data
- Probability theory
- Univariate random variables : discrete and continuous random variables, probability distributions
- Multivariate random variables : joint probability distributions, covariance, correlation and variance
- Estimation of parameters : random sample averages, random sample proportions, random sample variance
- Interval estimation : setting up of reliability intervals
- Hypothesis testing : after a general introduction on testing, we deal with the most important tests for location, dispersion and distribution for different measurement scales and for 1, 2 or more than 2 populations respectively.
- Parameter estimation

### 4 International dimension*

### 5. Teaching method and planned learning activities

Personal work

### 6. Assessment method and criteria

Permanent evaluation in the form of 2 multiple choice tests.

Examination

Continuous assessment

### 7. Study material *

#### 7.1 Required reading

Printed lecture notes available at the "cursusdienst". Additional examples, slides, exercises are provided via Blackboard.

**7.2 Optional reading**

The following study material can be studied voluntarily :There is no additional literature that the students should read.

### 8. Contact information *

mailto:Sandra.VanAert@uantwerpen.be

Annick.DeBacker@uantwerpen.be