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.

прочети още
Мрежови технологии (на английски език)

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:

  1. Combinatorics. Events and Sets. Sample space and probability mea- sures. Computing probabilities. Conditional probability and independence. Bayes theorem. Problems.
  2. Random variables. Discrete random variable and distributions. Continu- ous random variable and distributions. Normal distribution. Functions of random variables. Problems.
  3. 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.
  4. Generating functions and related problems.
  5. Joint Distributions. Discrete random variables. Continuous random variables. Independent random variables. Conditional distributions. Extrema and order statistics. Problems.
  6. The law of large numbers. The Central limit theorem. Distributions derived from the Normal distribution. Problems.
  7. Elements of the mathematical statistics. Basic conceptions. Objectives of the mathematical statistics. The large sample method. Empirical distribution functions. Histograms, frequency polygon. Problems.
  8. Estimation of the population parameters. Point estimates. The properties of the estimates. Maximum Likelihood and method of moments. Confidence intervals. Problems
  9. 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.
  10. 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%