Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Masterat
Domeniul: Informatica
Programul de studii: Modelare si simulare - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MMC1007	Computational Statistical Models	

Semester	Hours: C+S+L	Category	Status	
1	2+1+1	speciality	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
BLAGA Petru	Ph.D.	Prof.	Numerical and Statistical Calculus	*			

Associated faculty members
Name and	Scientific	Institution	Type of	Type of activity	
surname	title		position	C	S	L	

III. Course objectives
Knowledge and simulation of some statistical models oriented on software products. Correct using of the mathematical statistical models. Knowledge some statistical software. Development and construct of procedures for statistical methods.

IV. Course contents
&#8226; 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.
&#8226; Mean value and  covariance matrix of  random vector aleator. Conditional mean value. 
  Conditional varaince. Chebyshev inequality. Convegence in probability. Convergence in   
  distribution (law). Weak law of large numbers. Limit theorems (Lindeberg-Lévy, Moivre-
  Laplace, corrections of continuity). 
&#8226; Sampling theory. Sample functions. Sample mean. Sample moment. Sample central moment. 
  Sample variance. Sample distribution function. Glivenko theorem. Kolmogorov theorem.
&#8226; 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. 
&#8226; 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 &#8211; test and confidence interval  for variance of a variable. 
&#8226; Z-test, T-test and confidence intervals for difference of two mean values. F- test for 
  ratio of two variances.
&#8226; 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.
&#8226; Regression problem. Multiple linear model. Fitted least-squares multiple linear 
  regression model. Multiple linear model with constant term. Coefficient of 
  determination. Total variance equation.
&#8226; Gauss-Markov linear model. Gauss-Markov theorem. Unbiased estimators for coefficients. 
  Unbiased estimator for variance.
&#8226; 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.
&#8226; Maximum likelihood estimators for coefficients and variance.  Linear prediction 
  problem. Estimator for prediction. Confidence interval for prediction.
&#8226; 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.
&#8226; One-way analysis of variance. Total variance equation. F-test for equality of means of 
  categories. ANOVA table.
&#8226; 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.	

V. Bibliography
1. Agratini, O., Blaga, P., Coman, Gh., Lectures on Wavelets, Numerical Methods, and 
   Statistics, Casa Cărţii de Stiinţă, Cluj-Napoca, 2005.
2. Blaga, P., Calculul probabilităţilor şi statistică matematică. Vol. II. Curs şi 
   culegere de probleme, UBB, Cluj-Napoca, 1994.
3. Blaga, P., Statistică matematică. Lucrări de laborator, UBB, Cluj-Napoca, 1999.
4. Blaga, P., Statistica... prin Matlab, Presa Universitară Clujeană, Cluj-Napoca, 2002.
5. Blaga, P., Mureşan, A. S., Matematici aplicate în economie, Vol. I, Transilvania 
   Press, Cluj-Napoca, 1996.
6. Blaga, P., Rădulescu, M., Calculul probabilităţilor, UBB, Cluj-Napoca, 1987.
7. Iosifescu, M., Mihoc, Gh., Theodorescu, R., Teoria probabilităţilor şi statistica 
   matematică, Editura Tehnică, Bucureşti, 1966.
8. Mihoc, I., Calculul probabilităţilor şi statstică matematică, Part. I-II, UBB, Cluj-
   Napoca, 1994, 1995.
9. Văduva, I., Analiză dispersională, Editura Tehnică, Bucureşti, 1977.	

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
Final grade consists from:
&#8226; Final written exam:           50%
&#8226; Activity during the semester: 25% 
&#8226; Evaluation of homeworks:      25%

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Prof. BLAGA Petru, Ph.D.