Statistics I

General data

Course ID:	1000-135ST1
Erasmus code / ISCED:	11.203 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. / (0542) Statistics The ISCED (International Standard Classification of Education) code has been designed by UNESCO.
Course title:	Statistics I
Name in Polish:	Statystyka I
Organizational unit:	Faculty of Mathematics, Informatics, and Mechanics
Course groups:
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:	English
Type of course:	elective courses
Prerequisites:	Probability theory I 1000-114aRP1a
Short description:	The lecture is an introduction to mathematical statistics. We present theoretical foundations of statistical inference and discuss two essential topics of mathematical statistics - theory of estimation and theory of hypothesis testing.
Full description:	1. The notion of a statistical model, sample characteristics, the basic theorem of mathematical statistics. 2. Sufficient statistics, minimal sufficient statistics, complete statistics. 3. Estimation of distribution parameters: selected methods of estimation (maximal likelihood estimators, least squares method), properties of estimators (consistency, asymptotic normality, non-biased tests); comparison of estimators for the risk function corresponding to the quadratic loss function; non-biased estimators with minimal variance, information inequality. 4. Verification of statistical hypotheses: the notion of statistical test, error of 1st and 2nd kind, test power, Neyman-Pearson lemma, uniformly strongest tests for families with monotone confidence quotient, tests based on confidence quotient, hypothesis testing in normal models, non-parametric tests (Kolmogorov test and Wilcoxon test), chi-square test. 5. Confidence intervals
Bibliography:	P.J.Bickel, K.A.Doksum, Mathematical Statistics. Basic Ideas and Selected Topics. San Francisco 1977

This course is not currently offered.

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