Data analysis : Probability

Language

French

Prerequisites

The course has no prerequisites other than the mathematical background corresponding to a program of at least 4 hours of mathematics during the final years of secondary education. This course is reserved for enrolled students.

Main themes

The course covers traditional aspects of the probability theory but examines the concepts from the point of view of their use in statistical analysis. The probability model is described, as are the basic properties of probabilities. Then experiments are considered where the feature of interest can be modelled by a random variable (discreet, continuous, uni- and multivariate). The analysis of the random variable functions is presented and justified by its use in the analysis of statistic sampling distributions. The importance of the Central Limit Theorem is also highlighted.

Learning outcomes

At the end of this learning unit, the student is able to :
1	To introduce the probabilistic reasoning approach and the methods of statistical analysis. These methods are useful in all scientific fields where random and/or experimental aspects appear (human, technical, medical, or natural sciences). The course will mainly develop the tools useful for management sciences and economic and business sciences. At the end of the course, the student must be able to understand and model the random aspects of certain simple experiments and calculate the probabilities of the events of interest. They must also be able to apply these models to more complex real-world situations and describe these phenomena using appropriate random variables (univariate and multivariate). They will also see how to study the properties of functions of random variables and how these concepts naturally apply to the framework of statistical analysis (sampling). The contribution of this UE to the development and mastery of the skills and learning outcomes of the program(s) is accessible at the end of this sheet, in the section "Programs/courses offering this teaching unit." (LO of the program) Regarding the LSM Compass, the targeted skills are: Knowledge and reasoning. Regarding the Transition Wheel, the targeted skills are: Scientific knowledge and methods. Both concern the dimension Scientific knowledge and approach.

Content

• Introduction to statistics
  
• The probability model: calculating probabilities, conditional probabilities, combinatorics
  
• Discrete random variables, including the binomial, geometric and Poisson distributions
  
• Continuous random variables, including the uniform, exponential and normal distributions
  
• Discrete and continuous random vectors: marginal, conditional and joint distributions; correlation
  
• Transformations of random variables: order statistics, sums
  
• Random sampling and the central limit theorem: empirical mean and variance, approximation of the binomial distribution by the normal one
  

Teaching methods

The course is delivered in the form of:
• Lectures: The instructor defines concepts, demonstrates results, and illustrates them with an example or application.
• Exercise sessions: The instructor presents problems to the students and proposes a problem-solving approach. Students actively participate in solving the problems.

Evaluation methods

• Written exam on paper or computer. Exercises in the form of multiple-choice questions (MCQs) and/or numerical questions and/or open-ended questions.
• An optional exemption test covering part of the material, including exercises in the form of MCQs and/or numerical questions and/or open-ended questions, is organized during the semester if the health situation allows it.

Online resources

A list of formulas, additional exercises, solutions of exercises covered in the tutorials, and links to some useful websites are available on the MoodleUCL course page.

Teaching materials

• Wackerly, D., Mendenhall, W. and R. Scheaffer (2008), Mathematical Statistics with Applications, Duxbury Press, New York, 7th edition. (Chapitre 1 à 7)
• Syllabus "LINGE1113 - Probabilités" (J. Segers)

Faculty or entity

> ESPO