Mathematical statistics with applications 
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Teaching Staff in Charge 

Aims 
Knowledge of some moderns methods of mathematical statistics oriented to soft product (Matlab and Statgraphics). 
Content 
1. Normal distribution: Confidence limits and test hypotheses for mean, variance, difference of means and ratio of variances. Comparing two sample of equal size.
2. Parametric and nonparametric tests. 3. Regression: Simple linear regression. Mathematical model in liniar regression. Method of the least squares. Analysis of variance for linear regression. Estimations and predictions. Confidence intervals. Tests of hypotheses. 4. Multiple linear regression: Estimation of coefficients. Method of the least squares. Variances and covariances of the regression coefficients. Examination of residuals. Standard errors of predicted values. Analysis of variance. Confidence intervals and tests of hypotheses. 5. Analysis of variance (ANOVA): Oneway classification. Testing the equality of means. Equation of analysis of variance. ANOVA with unequal error variances. Multiple comparisons. Testing the equality of variances. Samples of unequal sizes. Twoway classification. ANOVA without replications. ANOVA in a balanced twoway layout with replications. Twoway ANOVA under heteroscedasticity. 
References 
1. LEBART, L.  MORINEAU, M.G.  FÉNELON, J.P.: Traitment des données statistiques. Paris: Dunod, 1982
2. LEHMANN, E.L.: Testing statistical hypotheses. New York: Springer, 1997. 3. MONTGOMERY, D.C.  PECK, E.A.  VINING, G.G.: Introduction to linear analysis. New York: John Wiley & Sons (3rd ed.), 2001. 4. SAPORTA, G.: Probabilités, analyse des données et statistique. Paris: Editions Technip, 1990. 5. TASSI, Ph.: Methodes statistiques. Paris: Economica (2nd ed.), 1989. 6. SCHERVISH, M.J.: Theory of statistics. New York: Springer, 1995. 7. STAPLETON, J.H.: Linear statistical models. New York: John Wiley & Sons, 1995. 8 .WEERAHANDI, S.: Exact statistical methods for data analysis. New York: Springer, 1994. 
Assessment 
Exam. 