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Probabilities and statistics

1EAG3 Probabilities and statistics Electronics and Applied Physics - Apprenticeship S6
Lessons : 10 h TD : 10 h TP : 6 h Project : 0 h Total : 26 h
Co-ordinator : Patricia Jouannot-Chesney
Prerequisite
Basic notions of combinatorial analysis and probabilities
Course Objectives
The objective of this course is to give a general control of most current statistical tools, based on a sufficient knowledge of the theoretical foundations of these tools.
Syllabus
I. Independance, conditional probabilities (Bayes' theorem)
II. Classical discrete (Poisson, binomial, geometric) and continuous (uniform, exponential, normal, chi-squared, Student... ) distributions and their main descriptors. Bivariate/Multivariate distributions.
III. Convergence and sampling : approximations of law, theorems (Law of large numbers, central limit theorem)
IV. Estimators for sample proportion, sample mean and sample variance
V. Hypothesis testing : comparison between two samples (t-test, Fisher-test), analysis of variance (ANOVA); chi-squared tests
Practical work (TD or TP)
Calculation of confidence intervals.
Estimation of an unknown parameter from a data sample.
Statistical comparison between two sets of data.
Goodness of fit tests.
Acquired skills
Engineers will be able to interpret the experimental results obtained in terms of statistics for various fields of activities.
Bibliography
HARTHONG J. Probabilités et statistiques de l'intuition aux applications, Bibliothèque des Sciences second cycle et grandes écoles, Diderot Editeurs, Arts et Sciences, 1996.
JAFFARD J. Initiation aux méthodes de la statistique et du calcul des probabilités, MASSON, 1996.
LECOUTRE JP. Statistique et probabilités, Dunod, 2016
PAROISSIN C. Programmation et analyse statistique avec R, Ellipses, 2015
SPIEGEL M.R. Statistique. Série Schaum, 1987.
http://mathworld.wolfram.com/
http://fr.wikipedia.org/wiki/Portail:Mathématiques

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