SubjectsSubjects(version: 861)
Course, academic year 2019/2020
  
Probability and statistics - O02310042
Title: Pravděpodobnost a statistika
Guaranteed by: Katedra matematiky a didaktiky matematiky (41-KMDM)
Faculty: Faculty of Education
Actual: from 2011
Semester: both
E-Credits: 4
Hours per week, examination: 2/2 C+Ex [hours/week]
Capacity: winter:unknown / unknown (999)
summer:unknown / unknown (999)
Min. number of students: unlimited
State of the course: not taught
Language: Czech
Teaching methods: full-time
Explanation: Rok4
Old code: PRST
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
you can enroll for the course in winter and in summer semester
Guarantor: RNDr. Dr. František Mošna
Classification: Mathematics > Probability and Statistics
Pre-requisite : OSOZ1M
Interchangeability : OB2310007
Annotation -
Last update: MOSNAF/PEDF.CUNI.CZ (24.10.2008)
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: MOSNAF/PEDF.CUNI.CZ (24.10.2008)

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: MOSNAF/PEDF.CUNI.CZ (29.09.2008)
  • Jiří Anděl : Matematická statistika , SNTL Praha 1985
  • A. Plocki, P. Tlustý : Pravděpodobnost a statistika pro začátečníky a mírně pokročilé, Prometheus Praha 2007
  • J. Likeš, J. Machek : Matematická statistika, SNTL Praha 1983
  • J. Likeš, J. Machek : Počet pravděpodobnosti, SNTL Praha 1987
  • A. A. Svěšnikov : Sbírka úloh z teorie pravděpodobnosti, matematické statistiky a teorie náhodných funkcí, SNTL Praha 1971
  • Josef Štěpán, Josef Machek : Pravděpodobnost a statistika pro učitelské studium, SPN Praha 1985 - skriptum
  • Pavel Charamza, Jan Hanousek : Moderní metody zpracování dat - statistika pro každého, Grada Praha 1991

Teaching methods -
Last update: MOSNAF/PEDF.CUNI.CZ (09.10.2008)

Lecture and seminar

Requirements to the exam -
Last update: MOSNAF/PEDF.CUNI.CZ (09.10.2008)
  • Credit requirements: active participation at seminars (80% attendance), homework, succesful completion of control tests
  • Exam requirements: knowledge of given definitions, understanding of definitions, connections, relations, ability to solve problems
Syllabus -
Last update: MOSNAF/PEDF.CUNI.CZ (06.02.2009)
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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