Universitatea Babeş-Bolyai Cluj-Napoca
Facultatea de Matematică şi Informatică
Ciclul de studii: Licenţă
Domeniul: Informatică
Programul de studii: Informatică - în limba engleză
Limba de predare: Engleză

SYLLABUS

I. General data
Code	Subject	
MMP0003	Probability Theory and Statistics	

Semester	Hours: C+S+L	Category	Status	
5	2+1+2	speciality	compulsory	

II. Full status faculty members
Name and	Scientific	Didactic	Chair	Type of activity	
surname	title	title		C	S	L	
MICULA Sanda	Ph.D.	Lect.	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
To acquire basic of Probability Theory and Mathematical Statistics, focusing on applications.	

IV. Course contents
1. Field of events. Operations with events. Pprobability space: classical definition of 
   probability, axiomatic definition of probability. Conditional probability. 
   Independent events. Total probability formula, Bayes formula. Classical probabilistic 
   models(Bernoulli, Poisson, Pascal, Markov-Polya). 
2. Random variables and discrete laws of probability (binomial, hypergeometric, Poisson, 
   Pascal, geometric). Distribution function. Continuous random variables. Probability 
   density function. Continuous laws of probability (uniform, normal, Gamma,  
   exponential, &#967;2, Beta, Student, Cauchy). Independent random variables. Operations 
   with random variables.
3. Numerical caracteristics for random variables. Expectation. Variance. Covariance and  
   correlation coefficient. Moments (initial, central, absolut, factorial). 
   Median, quantile, quartile, mode, skewness, kurtosis. Inegalities (Chebyshev, 
   Hölder, Cauchy-Schwartz-Buniakovski, Liapunov).
4. Convergence in probability, almost surely convergence, convergence in distribution. 
   Law of large numbers: Markov theorem, Chebyshev theorem, Poisson theorem, Bernoulli 
   theorem. Limit theorems: Lindeberg theorem, Liapunov theorem, Lindeberg-Lévy theorem, 
   Moivre-Laplace theorem.
5. Descriptive statistics. Statistical distribution. Parameters of statistical 
   distribution.
6. Sampling theory. Samples. Sample functions. Sample mean. Sample variance. Sample 
   moment. Sample central moment. Sample distribution function.Glivenko theorem.   
   Kolmogorov theorem.
7. Estimation theory. Estimating functions. Absolutely correct  and correct 
   estimators. Fisher information. Rao-Cramer inequality. Methods of estimation: method 
   of moments, method of maximum likelihood, method of confidence intervals. Monte Carlo 
   method.
8. Testing statistical hypotheses. Critical region. Power of a test. Neyman-Pearson 
   lemma. Z-test and  T (Student)-test for the mean. &#967;2-test for variance. F-test for 
   ratio of variances. Tests for difference of  means. &#967;2-test for several  
   characterstics. &#967;2-test for contingence tables. Goodness-of-fit-tests: Kolmogorov-
   Smirnov, &#967;2.	

V. Bibliography
1. Agratini, O., Blaga, P., Coman, Gh., Lectures on Wavelets, Numerical Methods and 
   Statistics, Casa Cărţii de Ştiinţă, Cluj-Napoca, 2005.
2. Blaga, P., Calculul probabilităţilor şi statistică matemmatică. Vol. II. Curs şi 
   culegere de probleme, Universitatea "Babeş-Bolyai" Cluj-Napoca, 1994. 
3. Blaga, P., Statistică prin Matlab, Presa Universitară Clujeană, Cluj-Napoca, 2002.
4. Blaga, P., Rădulescu, M., Calculul probabilităţilor, Universitatea "Babeş-Bolyai" 
   Cluj-Napoca, 1987. 
5. Ciucu, G., Craiu, V., Inferenţă statistică, Editura Didactică şi Pedagogică, 
   Bucureşti, 1974.
6. Feller, W.,  An introduction to probability theory and its applications, Vol.I-II,   
   John Wiley, New York, 1957, 1966.
7. Iosifescu, M., Mihoc, Gh.,. Theodorescu, R., Teoria probabilităţilor şi statistică 
   matematică, Editura Tehnică, Bucureşti, 1966. 
8. Lisei, H., Probability theory, Casa Cărţii de Ştiinţă, Cluj-Napoca, 2004.
9. Lisei, H., Micula, S., Soos, A., Probability Theory trough Problems and Applications, 
   Cluj University Press, 2006.
10. Shiryaev, A.N., Probability (2nd ed.), Springer, New York 1995.	

VI. Thematic of didactic activities per weeks

VII. Didactic methods used

VIII. Assessment
The final grade will be computed as follows:
  - final written exam at the end of semester: 50%
  - evaluation at the seminar:                 20%
  - lab works  during the semester:            30% 
Students who wish to improve their written exam grade, can do so in the oral exam.	

IX. Additional references

	Dean,							Chair head,

	Date,							Course responsible,
								Lect. MICULA Sanda, Ph.D.