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

Code	Subject	
MC268	Mathematical Statistics with Applications	

Section	Semester	Hours: C+S+L	Category	Type	
Applied Mathematics	2	2+1+1		optional	

Teaching Staff in Charge	Prof. BLAGA Petru, Ph.D., pblaga@cs.ubbcluj.ro	
Aims	Knowledge of some moderns methods of mathematical statistics oriented to soft product (Matlab), with applications in ecomomics, medicine, etc.	
Content	 Probability space. Random variables. Random vectors. Distribution function.    
  Probability density function. Conditional distribution function. Conditional 
  probability density function. Numerical characteristics of random variables. Mean 
  value. Variance.  Standard deviation. Covariance. Correlation coefficient. 
 Mean value and  covariance matrix of  random vector aleator. Conditional mean value. 
  Conditional variance. Chebyshev inequality. Convegence in probability. Convergence in 
  distribution (law). Weak law of large numbers. Limit theorems (Lindeberg-Lévy, Moivre-
  Laplace, corrections of continuity).
 Sampling theory. Sample functions. Sample mean. Sample moment. Sample central moment. 
  Sample variance. Sample distribution function. Glivenko theorem. Kolmogorov theorem.
 Estimation theory. Consistent estimator. Unbiased estimator. Absolutely correct 
  estimator. Correct estimator. Likelihood function. Maximum likelihood method. Maximim 
  likelihood estimator. Fisher information. Rao-Cramér inequality. Efficient estimator. 
  Method of  confidence intervals.
 Testing statistical hypotheses. Test for statistical hypothesis. Error of type I. 
  Error  of type II. Power of a test. Z-test, T-test and confidence interval for mean 
  value of a variable. &#967;2 - test and confidence interval  for variance of a variable. 
 Z-test, T-test and confidence intervals for difference of two mean values. F- test for 
  ratio of two variances.
 Goodness-of-fit &#967;2  - test for multinomial distribution.  Nonparametric goodness-of-
  fit &#967;2  - test. Parametric goodness-of-fit &#967;2  - test. Homogeneity  &#967;2  - test. 
  Independence &#967;2  - test. Goodness-of-fit Kolmogorov test. . Goodness-of-fit Kolmogorov-
  Smirnov test.
 Regression problem. Multiple linear model. Fitted least-squares multiple linear 
  regression model. Multiple linear model with constant term. Coefficient of 
  determination. Total variance equation.
 Gauss-Markov linear model. Gauss-Markov theorem. Unbiased estimators for coefficients. 
  Unbiased estimator for variance.
 Classical linear model. Probability law of the coefficient estimators. Probability law 
  of the variance estimator. T-test for the coefficients of  model, confidence intervals 
  for the coefficients of model.
 Maximum likelihood estimators for coefficiens and variance.  Linear prediction 
  problem. Estimator for prediction. Confidence interval for prediction.
 F-test for all coefficients. F-test for a subset of coefficients. F-test for classical 
  linear model with constant term. F-test for equality of some coefficients . F-test for 
  identity of two linear models. ANOVA table.
 One-way analysis of variance. Total variance equation. F-test for equality of means of 
  categories. ANOVA table.
 Analysis of variance with two and more factors. Two-way ANOVA without interaction. F-
  test for the null effect of a factor. Two-way ANOVA with interaction. F-test for the 
  null effect of a factor. F-test for the null interaction effects.	
Bibliography	1. AGRATINI, O., BLAGA, O., COMAN, Gh.: Lectures on Wavelets, Numerical Methods and 
   Statistics, Casa Cărţii de Ştiinţă, Cluj-Napoca, 2005.
2. BLAGA, P.: Statistică... prin Matlab, Presa Universitară Clujeană, Cluj-Napoca, 2002.
3. LEBART, L. - MORINEAU, M.G. - FÉNELON, J.-P.: Traitment des données statistiques. 
   Paris: Dunod, 1982
4. LEHMANN, E.L.: Testing statistical hypotheses. New York: Springer, 1997.
5. MONTGOMERY, D.C. - PECK, E.A. - VINING, G.G.: Introduction to linear analysis. New 
   York: John Wiley & Sons (3rd ed.), 2001.
6. SAPORTA, G.:  Probabilités, analyse des données et statistique. Paris: Editions 
   Technip, 1990. 
7. TASSI, Ph.: Methodes statistiques. Paris: Economica (2nd ed.), 1989.
8. SCHERVISH, M.J.: Theory of statistics. New York: Springer, 1995.
9. STAPLETON, J.H.: Linear statistical models. New York: John Wiley & Sons, 1995.
10.WEERAHANDI, S.: Exact statistical methods for data analysis. New York: Springer, 1994.	
Assessment	Final grade consists from:
 Final written exam :           50%
 Activity during the semester : 25% 
 Evaluation of homeworks :      25%