151-0087/01 – Probability and Statistics A ()

Gurantor departmentDepartment of Mathematical Methods in EconomicsCredits4
Subject guarantorFiktivní UživatelSubject version guarantorRNDr. Matěj Turčan, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semesterwinter
Study languageCzech
Year of introduction1992/1993Year of cancellation2006/2007
Intended for the facultiesEKFIntended for study typesMaster
Instruction secured by
LoginNameTuitorTeacher giving lectures
HAR30 Ing. Iva Harbichová
HOL21 RNDr. Michal Holčapek, Ph.D.
MAD30 RNDr. Anna Madryová, Ph.D.
TUR30 RNDr. Matěj Turčan, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit 2+2

Subject aims expressed by acquired skills and competences

Teaching methods

Summary

Taught only in Czech. There exists the corresponding subject Probability and Statistics A (151501) for English speaking students.

Compulsory literature:

1. Mendenhall, W. - Sincich, T.: Statistics for Engineering and the Sciences. New York, Macmillan Publishing Company, 1992. ISBN 0-02-946563-X. 2. Newbold, P.: Statistics for Business and Economics. London, Prentice-Hall Int. Lim., 1991. ISBN 0-13-850645-0. 3. Kvanli, A.H. - Pavur, R.J. - Guynes, C.S.: Introduction to Business Statistics - A Computer Integrated, Data Analysis Approach. New York, South- Western College Publishing, 2000. ISBN 0-324-01207-1. 4. Spiegel, M.R.: Theory and Problems of Probability and Statistics. Singapore, McGraws-Hill Book Co., 1985. ISBN 0-07-99030-1. 5. Walpole, R. A.: Introduction to Statistics. New York, Macmillan Publishers, 1989. ISBN 0-02-424150-4.

Recommended literature:

Way of continuous check of knowledge in the course of semester

E-learning

Další požadavky na studenta

Prerequisities

Subject has no prerequisities.

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Jevová algebra - základní pojmy (pokus, jev, relace a operace s jevy, zákony pro operace s jevy, systémy jevů). 2. Jevová algebra - dokončení (rozklad, jevové pole). Pravděpodobnost jevu - axiomatické zavedení, vlastnosti, definice. 3. Pravděpodobnost a operace s jevy (podmíněná pravděpodobnost, nezávislost jevů). 4. Bernoulliho posloupnost. Úplná pravděpodobnost a Bayesův vzorec. 5. Náhodná proměnná - definice, typy, zákon rozložení pravděpodobnosti (ZRP). Disktrétní náhodná proměnná (DNP) a popis jejího ZRP. 6. Typy rozložení DNP - binomické, hypergeometrické, geometrické, Poissonovo,... Aproximace binomického rozložení. 7. Spojitá náhodná proměnná (SNP) a popis jejího ZRP. Typy rozložení SNP - rovnoměrné, exponenciální,... 8. Normální rozložení SNP. Speciální (výběrová) rozložení (Pearsonovo, Studentovo, Fisher-Snedecorovo) 9. Charakteristiky rozložení náhodné proměnné. Klasifikace podle způsobu výpočtu a podle významu. 10. Dokončení charakteristik. Momentová vytvořující funkce. Přehled charakteristik základních typů rozložení. 11. Náhodný vektor (NV) - definice, zákon rozložení pravděpodobnosti, simultánní distribuční a frekvenční funkce, marginální a podmíněná rozložení složek, nezávislost složek. 12. Charakteristiky NV. 13. Korelační nůžky. Limitní věty: Čebyševova nerovnost, Zákon velkých čísel (Čebyševův a Bernoulliho), Lindeberg-Lévyho znění centrální limitní věty. 14. Typy statistických proměnných. Popis statistického souboru s jedním argumentem.

Conditions for subject completion

Full-time form (validity from: 1960/1961 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)
Min. number of points
Exercises evaluation Credit 85 (85) 0
        Written exam Written test 45  0
        Other task type Other task type 40  0
Mandatory attendence parzicipation:

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Occurrence in special blocks

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