Course: Probability and Statistics A

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Course title Probability and Statistics A
Course code KMA/PSA-A
Organizational form of instruction Lecture + Tutorial
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 6
Language of instruction English
Status of course Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Course availability The course is available to visiting students
Lecturer(s)
  • Šedivá Blanka, RNDr. Ph.D.
  • Kobeda Zdeněk, RNDr.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
Lectures in English only. 1. Introduction. Probability experiment, random event, the concept of probability, fundamental laws of probability, conditional probability. 2. Independence of events, Bayes theorem. Definition of random variable. Probability distribution of a random variable. Distribution function. 3. Important discrete distributions (binomial, hypergeometric, Poisson). 4. Important continous distributions (exponential, normal). 5. The central limit theorem. Quantiles. Function of random variable. 6. Random vector. Covariance and correlation. 7. Random sample. Descriptive statistics. Point estimate. Confidency intervals. 8. General procedure for testing hypotheses. Testing a claim about a mean. Tests of variances. 9. Chi-square test of goodness of fit. Contingency tables. 10. Correlation. Tests comparing two parameters. F-distribution. 11. Regression analysis. Coefficient of determination. Multiple regression. 12. Reliability function, failure rate. Weibull distribution. Sum of random variables. Gamma distribution. 13. Uses and abuses of statistics. Review. Conclusion.

Learning activities and teaching methods
Lecture with practical applications, Collaborative instruction, Self-study of literature
  • Contact hours - 65 hours per semester
  • Preparation for formative assessments (2-20) - 15 hours per semester
  • Preparation for comprehensive test (10-40) - 26 hours per semester
  • Preparation for an examination (30-60) - 50 hours per semester
prerequisite
professional knowledge
Students should have a basic knowledge of combinatorics (high school level) and basic knowledge of calculus of one real variable.
learning outcomes
On completion of this course the student will be able: - to describe random events and to compute their probabilities - to identify and describe continous or discrete random variable - to recognize basic types of discrete or continous distributions of probability - to use methods of descriptive statistics to summarize data - to enumerate point estimates and construct confidence intervals - to formulate statistical hypothesis and to choose an appropriate statistical test for its accception or rejection - to interpretate statistical results - to select an adequate plan for statistical experiments
teaching methods
Collaborative instruction
Self-study of literature
Lecture with practical applications
assessment methods
Combined exam
Test
Skills demonstration during practicum
Recommended literature
  • Bowerman, Bruce L.; O'Connell, Richard T. Applied statistics : improving business processes. Chicago : Irwin, 1997. ISBN 0-256-19386-X.
  • Brase, Charles Henry; Brase, Corrinne Pellillo. Understandable statistics : concepts and methods. Lexington : D.C. Heath, 1987. ISBN 0-669-12181-9.
  • Grimmett, Geoffrey R.; Stirzaker, David R. Probability and Random processes. Oxford : Oxford University Press, 2001. ISBN 0-19-857222-0.
  • Ross, Sheldon. A first course in probability. Prentice-Hall, New York, 2001. ISBN 978-0130338518.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences Mathematics for Science (2012) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 2 Winter
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2015) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2011) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics and Management (2011) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2016) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2015) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 2 Winter
Faculty of Applied Sciences Mathematics and its Applications (2017) Mathematics courses 2 Winter
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 2 Winter