## Babes-Bolyai University of Cluj-Napoca Faculty of Mathematics and Computer Science Study Cycle: Graduate SUBJECT

 Code Subject MMP0002 Mathematical Statistics
 Section Semester Hours: C+S+L Category Type Mathematics 5 2+2+1 speciality compulsory Mathematics and Computer Science 5 2+2+1 speciality compulsory Applied Mathematics 5 2+2+1 speciality compulsory
 Teaching Staff in Charge
 Prof. AGRATINI Octavian, Ph.D.,  agratinimath.ubbcluj.roAssoc.Prof. SOOS Anna, Ph.D.,  asoosmath.ubbcluj.roLect. LISEI Hannelore-Inge, Ph.D.,  hannemath.ubbcluj.ro
 Aims The use of the basic facts of the Statistics theory for some applications and the use of software in Statistics.
 Content 1. Descriptive statistics: Classification of data. Graphical representation of empirical distributions. Empirical moments. Empirical correlation and regression (Pearson, Spearman, Kendall, Friedman coefficients, regression problem, linear and non-linear regression, least squares method). 2. Sampling theory: Random sampling. Sampling functions. Mean. Variance. Standard deviation. Moments. Corrections for grouping. Correlation coefficient. Exact sampling distributions (Fisher's lemma, Student distribution, chi-square distribution, Fisher-Snedecor distribution). Asymptotic properties of sampling distributions (Gnedenko, and Kolomogorov theorems). 3. Theory of estimation: Estimators and estimations. Consistency. Point estimators. Unbiased estmator. Biased estimator. Sufficiency. Fisher's information. Rao-Cramer inequality. Minimum variance estimators. Efficiency. Methods of estimations (method of moments, method of maximum likelihood, confidence intervals method). 4. Testing statistical hypotheses: Simple and composite hypotheses, parametric and non-parametric tests. Power of statistical test. Test of simple hypotheses. Neymann's lemma. Most powerful test. Test of composite hypotheses. Testing of mean and difference of two means(Z-test, T-test). Testing of variance and ratio of two variances(chi-square-test, F-test). Chi-square test (multinomial distribution, goodness of fit, contingency tables, homogenity). Non-parametric tests (Kolmogorov test, Kolmogorov-Smirnov test).
 References 1. BLAGA, PETRU: Calculul probabilităţilor şi statistică matematică. Vol.II. Curs şi culegere de probleme. Cluj-Napoca: Universitatea "Babeş-Bolyai" Cluj-Napoca, 1994. 2. BLAGA, PETRU: Statistică matematică. Lucrări de laborator. Cluj-Napoca: Universitatea "Babeş-Bolyai" Cluj-Napoca, 1999. 3. BLAGA, PETRU: Statistică... prin Matlab. Cluj-Napoca: Presa Universitară Clujeană, 2002. 4. CIUCU, G. - CRAIU, V.: Introducere în teoria probabilităţilor şi statistică matematică. Bucureşti: Editura Didactică şi Pedagogică, 1971. 5. CIUCU, G. - CRAIU, V.: Inferenţă statistică. Bucureşti: Editura Didactică şi Pedagogică, 1974. 6. IOSIFESCU, M. - MIHOC, GH. - THEODORESCU, R.: Teoria probabilităţilor şi statistică matematică. Bucuresti: Editura Tehnică, 1966. 7. LEHMANN, E.L.: Testing statistical hypotheses. New York: Springer, 1997. 8. SCHERVISH, M.J.: Theory of statistics. New York: Springer, 1995. 9. SAPORTA, G.: Probabilités, analyse des données et statistique. Paris: Editions Technip, 1990. 10.TRÎMBIŢAŞ, RADU T.: Metode statistice. Cluj-Napoca: Presa Universitară Clujeană, 2000.
 Assessment Exam.
 Links: Syllabus for all subjects Romanian version for this subject Rtf format for this subject