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

    címtáras azonosítással

    vissza a tantárgylistához   nyomtatható verzió    

    Probability Theory

    A tantárgy neve magyarul / Name of the subject in Hungarian: Valószínűségszámítás

    Last updated: 2020. szeptember 5.

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

    Computer Engineering BSc

    Course ID Semester Assessment Credit Tantárgyfélév
    VISZAB02   2/2/0/v 5  
    3. Course coordinator and department Dr. Csákány Rita,
    Web page of the course
    4. Instructors

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

    Padmini Mukkamala    lecturer       Department of Computer Science and Information Theory

    5. Required knowledge

    Elementary combinatory, calculus

    6. Pre-requisites
    ((TárgyEredmény( "BMETE90AX21" , "jegy" , _ ) >= 2
    TárgyEredmény( "BMETE90AX04" , "jegy" , _ ) >= 2)

    ÉS NEM (TárgyEredmény("BMEVISZA208", "jegy", _) >= 2
    TárgyEredmény("BMEVISZA208", "felvétel", AktualisFelev()) > 0
    TárgyEredmény("BMEVISZAB00", "jegy", _) >= 2 )
    TárgyEredmény("BMEVISZAB00", "felvétel", AktualisFelev()) > 0
    TárgyEredmény( "BMEVISZAB00" , "aláírás" , _ ) = -1 )

    ÉS (Training.Code=("5N-A8") VAGY Training.Code=("5NAA8"))

    A fenti forma a Neptun sajátja, ezen technikai okokból nem változtattunk.

    A kötelező előtanulmányi rendek grafikus formában itt láthatók.

    7. Objectives, learning outcomes and obtained knowledge Learn the basics of stochastic modeling
    8. Synopsis


    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.


    9. Method of instruction

    2 hours lectures and 2 hours practices/week


    10. Assessment

    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%.


    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.

    11. Recaps


    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.


    12. Consultations

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

    13. References, textbooks and resources


    14. Required learning hours and assignment
    Preparation for lectures 8
     Preparation for practices 20
    Preparation for tests
    Preparation for exams
    15. Syllabus prepared by




    Dr. László Ketskeméty

    associate professor

    Department of Computer Science and Information Theory

    IMSc program

    IMSc score