NETB253 Теория на вероятностите
Анотация:
The course is an introduction to a probability theory and the foundation of mathematical statstics. The course covers the base terminology and concepts.
Преподавател(и):
проф. Димитър Атанасов д-р
гл. ас. Слав Ангелов д-р
Описание на курса:
Компетенции:
Students successfully finished this course will:
1) know:
Axioms and basic definitions of probability
Independence & conditional probability
Discrete and continuous random variables and the most frequency used distributions
Expectation & variance of a random variable, covariation and correlation
Law of large numbers and central limit theorem
Method of moments and maximum likelihood method in parameter estimations
Basic terms of hypothesis testing, Neyman-Pearson paradigm
Monte Carlo method
2) be able to:
Computing discrete and continuous probabilities
Compute expectations, variances, correlations
Apply the low of large numbers and the central limit theorem
Calculate point estimates of population parameters
Use Neyman-Pearson paradigm in hypotheses testing
Предварителни изисквания:
Basic knowledge on linear algebra and on mathematical analysis in the volume of the courses teaching in NBU
Форми на провеждане:
Редовен
Учебни форми:
Лекция
Език, на който се води курса:
Английски
Теми, които се разглеждат в курса:
- Combinatorics. Events and Sets. Sample space and probability mea- sures. Computing probabilities. Conditional probability and independence. Bayes theorem. Problems.
- Random variables. Discrete random variable and distributions. Continu- ous random variable and distributions. Normal distribution. Functions of random variables. Problems.
- Parameters of probability distributions. The expected value of a random variable. Expectations of functions of random variables. Expectations of linear combinations of random variables. Standard deviation and variance. A model of measurement error. Covariation and correlation. Conditional expectation and prediction. Problems.
- Generating functions and related problems.
- Joint Distributions. Discrete random variables. Continuous random variables. Independent random variables. Conditional distributions. Extrema and order statistics. Problems.
- The law of large numbers. The Central limit theorem. Distributions derived from the Normal distribution. Problems.
- Elements of the mathematical statistics. Basic conceptions. Objectives of the mathematical statistics. The large sample method. Empirical distribution functions. Histograms, frequency polygon. Problems.
- Estimation of the population parameters. Point estimates. The properties of the estimates. Maximum Likelihood and method of moments. Confidence intervals. Problems
- Testing statistical hypotheses. General notations. The Neyman-Pearson paradigm. The Neyman-Pearson lemma. Confidence intervals and testing hypotheses. Generalized likelihood ratio. Goodness-of-fit criteria. Prob- lems.
- Methods For Statistical Modeling. Monte Carlo Method. General description of the method. Pseudorandom numbers and sequences. Bootstrapping. Problems.
Литература по темите:
• Boslaugh S., Watters P. STATISTICS IN A NUTSHELL. O‘Reilly. 2008
• Chernick M. BOOTSTRAP METHODS: A GUIDE FOR PRACTITION-
ERS AND RESEARCHERS. Wiley 2007.
• Mendenhall W., T.Sincich, STATISTICS FOR THE ENGENEERING AND COMPUTER SCINCES, Dellen Publishing Company, San Fran- cisco, 1988.
• Mendenhall W., R.J. Beaver, INTRODUCTION TO PROBABILITY AND STATISTICS, Duxbury Press, Belmont, 1994.
• Feller W., AN INTRODUCTION TO PROBABILITY THEORY AND ITS APPLICATIONS,vol.1, 3rd ed. John Wiley & Sons, New York, 1970.
• Glyn J. et. al, MODERN ENGINEERING MATHEMATICS, 2nd ed., Addison-Wesley, Harlow-New York-Amsterdam, 2000.
• Grinstead C.M., J.L. Snell, INTRODUCTION TO PROBABILITY, 2nd electronic ed., http://www.dartmouth.edu/ chance.
• Knuth D.E., THE ART OF COMPUTER PROGRAMMING, VOL. 2 SEMINUMERICAL ALGORITHMS, Addison-Wesley, Harlow-New York- Amsterdam, 1969.
• Rice J.A., MATHEMATICAL STATISTICS AND DATA ANALYSIS, Wadsworth & Brooks, Pacific Grove, California, 1988.
• Shenon R.E., SYSTEMS SIMULATION: The art and science, Prentice- Hall, Inc., New Jersey, 1975.
Средства за оценяване:
RUNNING CONTROL: TERM EXAMS:
TESTS 30 % WRITTEN EXAM 50 %
PARTICIPATION IN SEMINARS 40 % ORAL EXAM 20 %
COURSE WORK/PROJECT .………... % EXAM ON PRACTICE 30%
ESSAY ...........… %
STUDY .………... %
CASUS ………..... %
OTHERS: 30%