# Probability and statistics

lfsab1105  2019-2020  Louvain-la-Neuve

Probability and statistics
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 + 30.0 h
Q1
Teacher(s)
Hainaut Donatien; von Sachs Rainer;
Language
English
Prerequisites
LFSAB1101 et LFSAB1102 or equivalent courses
Main themes
The course presents the fundamental concepts of probability and statistics that allow the student to solve the basic problems encountered in engineering  and to acquire the prerequisites to follow more advanced courses.
Aims
 At the end of this learning unit, the student is able to : 1 Contribution of the course to the program objectives: Regarding the learning outcomes of the program of Bachelor in Engineering, this course contributes to the development and the acquisition of the following learning outcomes: LO 1.1, 1.2 LO 2.3, 2.4, 2.6, 2.7 LO 4.1, 4.2, 4.3, 4.4 In virtue of the reference Learning outcomes (LO) of the program 'Master in Actuarial Sciences' , this activity will allow the student to have acquired Primarily the following AAs: AA1.1, AA1.2, AA1.3, AA2.4 Secondarily the following AAs: AA1.7, AA2.3 Specific learning outcomes of the course: More precisely, at the end of the course the students will be able to Use a scientific approach to extract reliable information from sampled data understand and know how to apply in various situations the basic concepts of probability and statistical inference develop simple probabilistic or empirical models for given observed phenomena and integrate these models into simulations evaluate and judge the credibility of a condition or a model present the results of an analysis including its level of uncertainty

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
Foundations of probability :
• Notion of and elementary calculus of probabilities; event, basic formulae for calculating probabilities, conditional probabilities, Bayes theorem, independence.
• Random variables: discrete and continuous random variables, probability distribution, distribution function, quantiles, expected values, variance, moments of k-th order.
• Classical probability laws: Bernoulli, binomial, Poisson, uniform, normal, exponential, gamma, '
• Bivariate random vectors: bivariate distribution, marginal and conditional distribution, conditional expectation and variance, independence of random variables, covariance and correlation.
• Transformation of random variables: expectation, variance and distribution of functions of random variables, linear combinations of common random variables.
Foundations of statistical inference :
• Point estimation and fitting of distributions: definition, quality of an estimator (bias, mean squared error), method of moment estimation, maximum likelihood method, least-squares method.
• Limit theorems: Central Limit Theorem, Law of Large Numbers;
• Confidence intervals: definition, construction using the method of pivotal functions, asymptotic confidence intervals.
• Hypothesis tests: concepts of hypotheses, general development of a test statistic and a decision rule, type 1 and type 2 error, p-value, Tests and confidence intervals for one or two samples in a normal population and for one or two proportions.
Statistical methods in engineering :
• Exploratory data analysis: mean, variance, standard deviation, median, interquartile range, correlation, Graphical summary of data: histogram, box plot'
• Analysis of Variance (one factor ANOVA): fixed model, as generalisation of a two-sample mean test.
• (Simple) Linear regression: least squares estimation, interpretation, tests and confidence intervals for the parameters, prediction, measures of goodness-of-fit, analysis of residuals.
Teaching methods
The course is made of several types of activities:
• oral presentations of the methodological concepts based on examples coming from the engineering world.
• exercise sessions (APE) where the student will be able to apply systematically the concepts presented in the course on well chosen examples.
• case studies (APP) where the student will be able to apply the statistical tools to real world data using software like Matlab or R.
The pedagogical approach encourages the student to work personally and have an active participation during the course.
Evaluation methods
Written individual exam of typically 3 hours duration, to evaluate the understanding of the treated concepts and techniques (exercises and theory, in form of multiple choice and open questions). Each student disposes of his own formular of 2 pages which summaries the essential equations. The APP receives a grade which counts for ~20% of the exam.
Other information
Required knowledges: mathematical analysis and calculus (differentiation and integration), matrix notation basic knowledge of MATLAB.
Bibliography
 Les transparents (sur iCampus) Documentations supplémentaires (sur iCampus) : Glossaire, tables, distributions, une introduction au logiciel MatLab, etc. L'ouvrage : "Mathematical Statistics with applications", D. Wackerly, W. Mendenhall III, R. Scheaffer.
Faculty or entity
BTCI

#### 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