# Probabilities and statistics (I)

lbir1212  2019-2020  Louvain-la-Neuve

Probabilities and statistics (I)
Note from June 29, 2020
Although we do not yet know how long the social distancing related to the Covid-19 pandemic will last, and regardless of the changes that had to be made in the evaluation of the June 2020 session in relation to what is provided for in this learning unit description, new learnig unit evaluation methods may still be adopted by the teachers; details of these methods have been - or will be - communicated to the students by the teachers, as soon as possible.
4 credits
30.0 h + 15.0 h
Q1
Teacher(s)
Language
French
Prerequisites
LBIR1110  Math I
LMAT1111E  Math II

The prerequisite(s) for this Teaching Unit (Unité d’enseignement – UE) for the programmes/courses that offer this Teaching Unit are specified at the end of this sheet.
Main themes
Introduction to the calculus of probability - Discrete and continuous random variables: probability and probability density functions, expectations, variance and other statistical properties - Principal statistical distributions - Couples of random variables and random vectors: joint, marginal and conditional distributions, independence, covariance and correlation, expectations and conditional variance - Introduction to statistics - Notions concerning estimators and estimator properties - Inference about the mean and variance: estimators, sample distributions - Notions of one-mean-confidence intervals.
Aims
 At the end of this learning unit, the student is able to : 1 a.     Contribution of this activity to the learning outcomes referential : 1.1, 2.1 b.     Specific formulation of the learning outcomes for this activity A the end of this activity, the student is able to : ·       Name, describe and explain the theoretical concepts underlying the probability theory; ·       Use the mathematical expressions in a formal way and by using rigorous notations in order to deduce new expressions or requested theoretical results; ·       Translate mathematically textual statements using a rigorous mathematical and probabilistic framework by relying on appropriate concepts and theoretical tools; ·       Solve an applied problem by using a deductive approach that relies on a correct use of well identified properties and expressions; ·       Validate the internal consistency of the mathematical expressions and results based on theoretical properties and logical constraints that are induced by the probabilistic framework;

The contribution of this Teaching Unit to the development and command of the skills and learning outcomes of the programme(s) can be accessed at the end of this sheet, in the section entitled “Programmes/courses offering this Teaching Unit”.
Content
Introduction to the calculus of probability - Discrete and continuous random variables: probability and probability density functions, expectations, variance and other statistical properties - Principal statistical distributions - Couples of random variables and random vectors: joint, marginal and conditional distributions, independence, covariance and correlation, expectations and conditional variance - Introduction to statistics - Notions concerning estimators and estimator properties - Inference about the mean and variance: estimators, sample distributions. Notion of confidence intervals.
Teaching methods
Regular courses and supervised practical exercises
Evaluation methods
Evaluation: Open book written examination (only with the original material). The examination is composed of exercises to be solved. Its duration is about 3 hours.
Other information
The course relies on a book which is considered as mandatory and must be bought :
P. Bogaert (2005). Probabilités pour scientifiques et ingénieurs. Editions De Boeck
Online resources
Moodle
Faculty or entity

#### Programmes / formations proposant cette unité d'enseignement (UE)

Title of the programme
Sigle
Credits
Prerequisites
Aims
Interdisciplinary Advanced Master in Science and Management of the Environment and Sustainable Development

Master [120] in Environmental Science and Management

Bachelor in Bioengineering
4

Bachelor in Computer Science

Master [120] in Data Science : Statistic

Minor in Statistics, Actuarial Sciences and Data Sciences