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.
At the end of this learning unit, the student is able to :
Contribution of the course to the program objectives:
In virtue of the reference Learning outcomes (LO) of the program ¿Master in Actuarial Sciences¿ , this activity will allow the student to have acquired
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”.
- 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.
- 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.
- 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.
- 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.
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.