MMC1003  Mathematical Statistics with Applications 
Teaching Staff in Charge 
Prof. BLAGA Petru, Ph.D., pblagacs.ubbcluj.ro 
Aims 
Knowledge of some moderns methods of mathematical statistics oriented to soft products.

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 varaince. Chebyshev inequality. Convegence in probability. Convergence in distribution (law). Weak law of large numbers. Limit theorems (LindebergLévy, 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. RaoCramér 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. Ztest, Ttest and confidence interval for mean value of a variable. χ2 – test and confidence interval for variance of a variable. • Ztest, Ttest and confidence intervals for difference of two mean values. F test for ratio of two variances. • Goodnessoffit χ2test for multinomial distribution. Nonparametric goodnessoffit χ2test. Parametric goodnessoffit χ2test. Homogeneity χ2test. Independence χ2test. Goodnessoffit Kolmogorov test. Goodnessoffit KolmogorovSmirnov test. • Regression problem. Multiple linear model. Fitted leastsquares multiple linear regression model. Multiple linear model with constant term. Coefficient of determination. Total variance equation. • GaussMarkov linear model. GaussMarkov theorem. Unbiased estimators for coefficients. Unbiased estimator for variance. • Classical linear model. Probability law of the coefficient estimators. Probability law of the variance estimator. Ttest for the coefficients of model, confidence intervals for the coefficients of model. • Maximum likelihood estimators for coefficients and variance. Linear prediction problem. Estimator for prediction. Confidence interval for prediction. • Ftest for all coefficients. Ftest for a subset of coefficients. Ftest for classical linear model with constant term. Ftest for equality of some coefficients . Ftest for identity of two linear models. ANOVA table. • Oneway analysis of variance. Total variance equation. Ftest for equality of means of categories. ANOVA table. • Analysis of variance with two and more factors. Twoway ANOVA without interaction. F test for the null effect of a factor. Twoway ANOVA with interaction. Ftest for the null effect of a factor. Ftest for the null interaction effects. 
References 
1. Agratini, O., Blaga, P., Coman, Gh., Lectures on Wavelets, Numerical Methods, and
Statistics, Casa Cărţii de Stiinţă, ClujNapoca, 2005. 2. Blaga, P., Calculul probabilităţilor şi statistică matematică. Vol. II. Curs şi culegere de probleme, UBB, ClujNapoca, 1994. 3. Blaga, P., Statistică matematică. Lucrări de laborator, UBB, ClujNapoca, 1999. 4. Blaga, P., Statistica... prin Matlab, Presa Universitară Clujeană, ClujNapoca, 2002. 5. Blaga, P., Mureşan, A. S., Matematici aplicate în economie, Vol. I, Transilvania Press, ClujNapoca, 1996. 6. Blaga, P., Rădulescu, M., Calculul probabilităţilor, UBB, ClujNapoca, 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. III, UBB, Cluj Napoca , 1994, 1995. 9. Văduva, I., Analiză dispersională, Editura Tehnică, Bucureşti, 1977. 
Assessment 
Final grade consists from:
• Final written exam : 50% • Activity during the semester : 25% • Evaluation of homeworks : 25% 
Links:  Syllabus for all subjects Romanian version for this subject Rtf format for this subject 