SubjectsSubjects(version: 849)
Course, academic year 2019/2020
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Statistics and Probability - OB2310N217
Title in English: Statistika a pravděpodobnost
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2012
Semester: summer
E-Credits: 4
Examination process: summer s.:written
Hours per week, examination: summer s.:1/2 MC [hours/week]
Capacity: unknown / unknown (unknown)
Min. number of students: unlimited
State of the course: taught
Language: Czech
Teaching methods: full-time
Note: course can be enrolled in outside the study plan
enabled for web enrollment
priority enrollment if the course is part of the study plan
Guarantor: RNDr. František Mošna, Dr.
Class: Matematika 1. cyklus - povinné
Classification: Mathematics > Mathematics, Algebra, Differential Equations, Potential Theory, Didactics of Mathematics, Discrete Mathematics, Math. Econ. and Econometrics, External Subjects, Financial and Insurance Math., Functional Analysis, Geometry, General Subjects, , Real and Complex Analysis, Mathematics General, Mathematical Modeling in Physics, Numerical Analysis, Optimization, Probability and Statistics, Topology and Category, Probability and Statistics
Pre-requisite : OB2310N004
Interchangeability : OB2310217
Annotation -
Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)
Random trial, random event, probability, distribution of probablity, probability density, distribution function. Operations with random variables, Law of great numbers, central limit theorem. Distribution: normal, chi-square, Student. Testing hypotheses, statistical tests, data processing
Aim of the course -
Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)

Primary purpose of the course is to make students acquainted with probability models and basics of stochatic model. Secondary aim is to show the students statistics methods, teach them to use these methods correctly and interpret them in concrete situations. Tertiary aim is to show the usefulness of previous courses (mainly mathematic analysis) during the derivation of statements, theorems and formulas.

Literature -
Last update: RNDr. František Mošna, Dr. (22.03.2018)

- F. Mošna: Pravděpodobnost a náhodné veličiny, PedF UK Praha 2017 
- F. Mošna: Základní statistické metody, PedF UK Praha 2017
- J. Štěpán, J. Machek : Pravděpodobnost a statistika pro učitelské studium, SPN Praha 1985 - skriptum

- J. Anděl : Matematická statistika , SNTL Praha 1985
- J. Brousek, Z. Ryjáček: Sbírka řešených příkladů z počtu pravděpodobnosti, ZČU Plzeň 1995
- P. Charamza, J. Hanousek : Moderní metody zpracování dat - statistika pro každého, Grada Praha 1991
- A. Plocki, P. Tlustý : Pravděpodobnost a statistika pro začátečníky a mírně pokročilé, Prometheus Praha 2007
- J. Reif: Metody matematické statistiky, ZČU 2000

Teaching methods -
Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)

Seminars.

Requirements to the exam -
Last update: MOSNAF/PEDF.CUNI.CZ (07.03.2013)

graded credit  - adequate active participation in seminars, two tests will be written during the semester, the first will focus on understanding the basic concepts, relationships and contexts related to probability, tn the second  the student demonstrate the ability to appropriate handle with the bulk data and to main the information from them using discussed tests    

Syllabus -
Last update: JANCARIK/PEDF.CUNI.CZ (17.05.2012)
Probability
  • random trial, random event, probability(classical, geometrical), recapitulation of elements of combinatorics
  • independence of random events, conditional probability, complete probability theorem, the theorem of Bayes
  • random variables and distribution of probability, expected value, variance, other characteristics
  • discrete and continuos distributions (alternative, binomial, hypergeometric, geometric, Poisson, uniform, exponential), probability density, distribution function
  • random vectors, joint and marginal probability density and distribution function
  • independence of random variables, covariance, corellation
  • operation with random variables, Law of the great numbers, central limit theorem, normal distribution, distribution chi-square, Student, Fischer
Statistics
  • random sample, parameter estimate, testing hypotheses principle, statistical discrepancy
  • basic types of statistic tests (t-test, one-sample, two-sample, corellation coefficient)
  • linear regression, method of least squares
  • analysis of variance
  • contingency table, some other tests (McNemar), Pearson's chi-square test
  • non-parametric methods (sign test, Wilcoxon test, Spearmann coefficient)
  • descriptive statistics, data processing
 
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