## NETB253 Probability Theory

### Анотация:

" The course is a short introduction in the classical and contemporary conceptions of probability theory. It includes the most important topics of the probability and mathematical statistics:

ў Basic ingredients of probability theory and elementary combinatorial methods using non-measure approach.

ў Concepts of random variable and its probability distribution

ў Expectations, variance, covariance, correlation and moment-generating functions

ў The low of large numbers and the central limit theorem

ў The idea of an estimate as a random variable with an associate sampling distribution

ў Neyman-Pearson approach to hypotheses testing

ў Method for modeling random variables (Monte Carlo method)

" The course objectives are:

ў to give the students a conceptual understanding of the basic probability terms and procedures

ў to help the students in achieving those computational skills need to carry out probability calculations in practical settings

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### Преподавател(и):

доц. Димитър Атанасов  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

### 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%