M3121 Probability and Statistics I

Faculty of Science
Autumn 2007 - for the purpose of the accreditation
Extent and Intensity
2/2/0. 4 credit(s) (fasci plus compl plus > 4). Type of Completion: z (credit).
Teacher(s)
RNDr. Marie Forbelská, Ph.D. (lecturer)
prof. RNDr. Gejza Wimmer, DrSc. (lecturer)
doc. Mgr. Kamila Hasilová, Ph.D. (seminar tutor)
doc. Mgr. Jan Koláček, Ph.D. (seminar tutor)
RNDr. Tomáš Pavlík, Ph.D. (seminar tutor)
Mgr. Jaroslava Sidorová (seminar tutor)
Guaranteed by
prof. RNDr. Ivanka Horová, CSc.
Department of Mathematics and Statistics – Departments – Faculty of Science
Contact Person: prof. RNDr. Ivanka Horová, CSc.
Prerequisites
M2100 Mathematical Analysis II || FI:MB001 Calculus II
Differential and integral calculus of functions of n real variables. Basic knowledge of linear algebra.
Course Enrolment Limitations
The course is also offered to the students of the fields other than those the course is directly associated with.
fields of study / plans the course is directly associated with
Course objectives
The basic course of probability and mathematical statistics and introductory course for other theoretically oriented and applied stochastic subjects. The content of the course is axiomatical approach to probability theory, random variables and random vectors, probability distributions and characteristics of the distribution. The last part of the course is dovoted to the laws of large numbers and to the central limit theorem.
Syllabus
  • Elements of probability: axiomatic definition of probability, probability space, conditional probability, independence. Random variables: borel functions, definition of random variable, distribution function, discrete and continuous probability distributions, probability and density function, examples of discrete and continuous random variables, distribution of transformed random variables, pseudorandom numbers. Random vectors: joint distributions, independence, examples of multivariate distributions (multivariate normal and multinomial distributions), distribution of the sum and ratio of random variables, distributions derived from normal distribution, marginal and conditional distributions. Characteristics: expectation, variance, covariance, moments and their properties, covariance and correlation matrices, characteristic function of random vector. Limit theorems: Borel and Cantelli theorem, Cebyshev's inequality, Laws of large numbers, central limit theorem.
Literature
  • Ash, R.B. and Doléans-Dade C.A. Probability and measure theory. Academic Press. San Diego.2000
  • MICHÁLEK, Jaroslav. Úvod do teorie pravděpodobnosti a matematické statistiky. Vyd. 1. Praha: Státní pedagogické nakladatelství, 1984, 204 s. info
  • Karr, A.F. Probability. Springer. 1992
  • Dupač, V. a Hušková, M.: Pravděpodobnost a matematická statistika. Karolinum. Praha 1999.
Assessment methods (in Czech)
Výuka: přednáška, klasické cvičení. Zkouška písemná a ústní.
Language of instruction
Czech
Follow-Up Courses
Further comments (probably available only in Czech)
The course can also be completed outside the examination period.
The course is taught annually.
The course is taught: every week.
Listed among pre-requisites of other courses
The course is also listed under the following terms Autumn 2010 - only for the accreditation, Autumn 2002, Autumn 2003, Autumn 2004, Autumn 2005, Autumn 2006, Autumn 2007, Autumn 2008, Autumn 2009, Autumn 2010, Autumn 2011, Autumn 2011 - acreditation, Autumn 2012, Autumn 2013, Autumn 2014, Autumn 2015, Autumn 2016, autumn 2017, Autumn 2018, Autumn 2019, Autumn 2020, autumn 2021, Autumn 2022, Autumn 2023, Autumn 2024.