## DMS212 Probability Theory and Mathematical Statistics

 Code DMS212 Name Probability Theory and Mathematical Statistics Status Compulsory/Courses of Limited Choice Level and type Undergraduate Studies, Academic Field of study Mathematics and Statistics Faculty Academic staff Oksana Pavļenko, Kārlis Šadurskis, Andrejs Matvejevs, Nataļja Budkina, Aija Pola, Māris Buiķis, Marija Dobkeviča, Daina Pūre, Vaira Buža, Jolanta Goldšteine, Jeļena Mihailova Credit points 2.0 (3.0 ECTS) Parts 1 Annotation Classical definition of probability. Axiomatic definition of probability. Algebra of events. Bernully's scheme. Formulas of complete probability and Baijes. Continuous and discrete random variable. Distributive and density of functions. Large numbers law. Central limit theoreme. Elements of mathematical statistics. Combinatoric. Test of hypothesis.. Goals and objectives of the course in terms of competences and skills The objective of the course is to acquaint students with basics of probability theory and its mathematical apparatus both on the classical scheme level, and also on axiomatic level. Allow to understand the regularities of the random phenomena that occur mass-repeating. Giving an overview of mathematical statistics mission and the possibility of using probability theory apparatus to solve them. Learning outcomes and assessment Calculation of probabilities for random events. Application of probability axioms, classical definition, conditional probability, total probability and Bayes' and Bernoulli formulae - Problems to be solved included in test 1 Random variables. Application of major facts on probability distributions (discrete and continuous), distribution function, density, numeric characteristics. - Problems to be solved included in test 2 Elements of mathematical statistics. Application of statistical estimates and confidence intervals, major methods, hypotheses testing, losses, risk, form of criteria based on Neyman - Pearson lemma, characteristics of criteria. - Problems to be solved included in the exam Course prerequisites Linear algebra and analytic geometry, calculus.

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