Probability theory and statistics

General data

Course ID:	1000-213bRPS
Erasmus code / ISCED:	11.302 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. / (0612) Database and network design and administration The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Probability theory and statistics
Name in Polish:	Rachunek prawdopodobieństwa i statystyka
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:	Obligatory courses for 2nd grade Computer Science
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:	Basic introduction to probability theory and statistics as well as popular statistics software.
Full description:	* Probability space: axioms of probability; properties of probability spaces; classical definition of probability; probability measures. * Conditional probability and independence: definition of conditional probability, Law of Total Probability, Bayes' Theorem, independence of events. * Discrete random variables: definition, properties, basic probability distributions - two-point, binomial, Poisson, geometric. * Basic probability distributions: Bernoulli, binomial, Poisson, geometric, normal, exponential. * Parameters of probability distributions: expected value, variance, higher moments. * Inequalities and limit theorems: Markov Inequality, Chebyshev Inequality, Law of Large Numbers, Central Limit Theorem. * Continuous random variables: definition, properties, exponential and normal distributions, Central Limit Theorem. * Markov chains: definition and basic properties, classification of states, ergodicity, applications. * Descriptive statistics: features and their scales, raw and cumulative data, graphical presentation, measures of central tendency and dispersion. * Statistical reasoning: samples, statistics and estimators, parametric vs nonparametric estimation, maximum likelihood method. * Hypothesis testing and confidence intervals: confidence intervals for the mean, confidence levels and p-values, methodology of a statistical test.
Bibliography:	(in Polish) 1. J. Jakubowski, R. Sztencel, Rachunek prawdopodobieństwa dla prawie każdego, Script, Warszawa 2006. 2. W. Krysicki i współautorzy, Rachunek prawdopodobieństwa i statystyka matematyczna w zadaniach , część I, II, Wydawnictwo Naukowe PWN, Warszawa 2004. 3. W. Feller, Wstęp do rachunku prawdopodobieństwa , Wydawnictwo Naukowe PWN, Warszawa 2006. (dla chętnych)
Learning outcomes:	Knowledge: 1. Has knowledge in the area of mathematics, involving probabilistic methods and statistics (especially discrete methods) (K_W01). 2. Understands the basic probabilistic techniques used in algorithm design (K_W02). Abilities 1. Is able to formalize given random events using probabilistic spaces (K_U09). 2. Is able to conduct statistical analysis using available computer programs (K_U05). Competences 1. Knows the and understands the need of further education (K_K01). 2. Is able to manage their time, undertake responsibilities and fulfill time constraints (K_K05).
Assessment methods and assessment criteria:	The following elements are required: - A partial exam during the semester. - A lab project in statistics: It is required to write 4 programs in the language Python. This projects verifies the student's ability to perform a statistical analysis in practice. - Exam. Exam consists of a theoretical test, and problems. To attend the first term, one needs to pass the partial exam and the lab project before the deadline. To attend the second term, one needs to pass the lab project before the exam in the second term.

This course is not currently offered.

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