# Probabilities and statistics (I)

lbir1212  2020-2021  Louvain-la-Neuve

Probabilities and statistics (I)
Due to the COVID-19 crisis, the information below is subject to change, in particular that concerning the teaching mode (presential, distance or in a comodal or hybrid format).
4 credits
30.0 h + 15.0 h
Q1
Teacher(s)
Language
French
Prerequisites
LBIR1110
LBIR1111

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;
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

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

Regular courses and supervised practical exercises
Evaluation methods

Due to the COVID-19 crisis, the information in this section is particularly likely to change.

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
Master [120] in Data Science : Statistic

Minor in Statistics, Actuarial Sciences and Data Sciences

Bachelor in Bioengineering
4

Interdisciplinary Advanced Master in Science and Management of the Environment and Sustainable Development

Bachelor in Computer Science

Master [120] in Environmental Science and Management