Budapest University of Technology and Economics, Faculty of Electrical Engineering and Informatics

Márta Barbara Pintér  associate professor  Department of Computer Science and Information Theory

Padmini Mukkamala    lecturer       Department of Computer Science and Information Theory

Elementary combinatory, calculus

A kötelező előtanulmányi rend az adott szak honlapján és képzési programjában található.

1.      Historical introduction. Basic concepts: random experiment, event space, event, elementary event, operation between events, axioms, sigma algebra

2.      Properties of probability: Poincare-rule, Boole’s inequalities, continuity of probability

3.      Conditonial probability, independency of events, Theorem of total probability, Bayes’s Theorem, produce theory

4.      Classical probability, geometrical probability. Examples for application: urn models, Buffon’s needle

5.      Random variable, probability distribution function, discrete and continouos cases, properties of the distribution function, probability of falling in an interval, discrete distribution, probability density function

6.      Notable discrete random variables: binomial, Poisson, geometrical.  Poisson approximation to the binomial distribution. Memoryless properties of the geometric distribution

7.      Notable continouos distributions: uniform, exponential, normal. Simulation with uniform distribution. Memoriless property of the exponential distribution. Standard normal distribution. Linear transformation

8.      Expected value, deviation, moments.  Theorems for expected value and deviation. Expected value and deviation of notable dispersions.

9.      Steiner’s Theorem, Markov’s- and Chebisev’s inequalities.

10.  Joint distribution function, projective distribution functions. Independency, convolution (discrete and continouos cases), Joint density function, projective density function

11.  Theorems of large numbers: Weak- and Stronge Law of Large Numbers. Central limit theorems, Moivre-Laplace’s Theorem

12.  Covariance, correlation. Properties of covariance and correlations. Connection between independency and uncorrelatedness

13.  Conditional distribution, conditional expectation (regression). Linear regression. Properties of regression. Examples of discrete and continouos cases.

14. Two-dimensional normal distribution,  polynomial distribution. Connection of the independency and uncorrelatedness in normal case. Projections of the polinomial distribution are binomials.

2 hours lectures and 2 hours practices/week

Period of study:

Participation in the exercises is compulsory (TVSZ § 14 (3) in Code of studies and exams).
During the semester, a 120-point midterm test run will be written,  at least 40 points are required for the signature.

Exam period:

A 120-point final test run will be written, at least 40 points are required to pass the exam. The results of the semester interim test result and the examination result are included in the test result at ratio 40% -60%.

Evaluation:

total score = 0.4*min(Midterm;100) + 0.6*min(Final;100).

If the total score is        40-54 points sufficient (2),

55-69 points medium (3),

70-84 points good (4),

85-100 marks (5).

In case of written exam’s result at least sufficient, it is possible to change 1 mark upwards and downwards, depending on the oral exam.

The repetition option for the midterm test: the inadequate result can be improved or the missing result can be replaced in a retake test. If the student has not written a midterm test, writing the retake midterm test is compulsory. Without writing this he or she will not get signature from the subject. If someone has failed the midterm test, but does not participate in the substitution occasion, can try to get the signature for a replacement fee in the first week of the exam period.

At the retake midterm test it is also possible to try to improve the reached results in case of a successful midterm test’s result. The valid result will be the greater one among the new result and 40.The new score will be valid even if it is worse than the original. A valid result already cannot be improved in the exam period.

During the semester at the lecturer's scheduled reception hours. We organize consultations before midterm tests and exams.