Probability theory I

General data

Course ID:	1000-114bRP1b
Erasmus code / ISCED:	11.1 Kod klasyfikacyjny przedmiotu składa się z trzech do pięciu cyfr, przy czym trzy pierwsze oznaczają klasyfikację dziedziny wg. Listy kodów dziedzin obowiązującej w programie Socrates/Erasmus, czwarta (dotąd na ogół 0) – ewentualne uszczegółowienie informacji o dyscyplinie, piąta – stopień zaawansowania przedmiotu ustalony na podstawie roku studiów, dla którego przedmiot jest przeznaczony. / (0541) Mathematics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Probability theory I
Name in Polish:	Rachunek prawdopodobieństwa I (potok 2)
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	Obligatory courses for 2nd grade JSEM Obligatory courses for 2nd grade JSIM (3M+4I) Obligatory courses for 2rd grade Mathematics Obligatory courses for 3rd grade JSIM (3I+4M)
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	Polish
Type of course:	obligatory courses
Short description:	Kolmogorov axioms. Basic probabilities. Random variables, probability distributions, and their parameters. Independence. Convergence of random variables. Basic limit theorems: Poisson theorem, weak and strong laws of large numbers, de Moivre-Laplace theorem.
Full description:	Kolmogorov axioms. Properties of probability measures. Borel-Cantelli lemma. Conditional probability. Bayes' theorem.. Basic probabilities: classical probability, discrete probability, geometric probability. Random variables (one- and multidimensional), their distributions. Distribution functions. Discrete and continuous distributions. Distribution densities. Parameters of distributions: mean value, variance, covariance. Chebyshev inequality. Independence of: events, ?-fields, random variables. Bernoulli (binomial) process. Poisson theorem. Distrubution of sums of independent random variables. Convergence of random variables. Laws of large numbers: weak and strong. De Moivre-Laplace theorem.
Bibliography:	Billingsley, P., Probability and Measure. Feller, W., An introduction to probability theory and its applications. vol. I, II, Shiryayev, A. N., Probability, New York : Springer-Verlag, 1984.

This course is not currently offered.

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