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

1.      Historical introduction. Elementary combinatorics: permutation, combination, variation.

Basic concepts: random experiment, event space, event, elementary event, operation between events, axioms

2.      Properties of probability: Poincare-rule, Boole’s inequalities, classical and geometrical probability field

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

4.   Random variable, probability distribution function, discrete distribution, expected value. Binomial, Poisson, geometrical distribution. Approximation of the Poisson distribution by the binomial distribution.

5.   Continouos cases, properties of the distribution function, probability density function, expected value, transformation of random variables.

6.   Notable continouos distributions: uniform, exponential. Simulation with uniform distribution. Memoriless property of the exponential and the geometric distribution. Variance, moments.

7.    Joint distribution function, projective distribution functions. Independency. Joint density function, projective density function. Covariance, correlation.

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

9.   Basics of mathematical statistics: sample, parameter, statistics. Properties of estimation: unbiased, consistency, efficiency

10. Estimation of average and variance, maximum likelihood, method of moments, nonparametric methods, empirical distribution function, regression estimation

11.  Theorems of large numbers, Markov’s- and Chebisev’s inequalities.

12.  Normal distribution, standardization. Central limit theorems, Moivre-Laplace’s Theorem

13.  Two-dimensional normal distribution. Connection of the independency and uncorrelatedness in normal case. Regression in case of normal distribution.

Period of study:

 There will three 20-points level tests be written during the exercises, the sum of the points of the two best tests must be at least 20 in order to get the signature.

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 level tests can not be repeated.

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.