Course: Statistical Analysis 1

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Course title Statistical Analysis 1
Course code KMA/SA1
Organizational form of instruction Lecture + Not exists
Level of course Bachelor
Year of study not specified
Semester Winter
Number of ECTS credits 5
Language of instruction Czech
Status of course Compulsory, Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Šedivá Blanka, RNDr. Ph.D.
  • Vávra František, Doc. Ing. CSc.
  • Tomiczková Světlana, RNDr. Ph.D.
Course content
Probability terms I., continuous variables. Probability terms II., discrete variables. Sampling distributions I., gamma distribution, beta distribution, Student?s t-distribution, F-distribution. Sampling distribution II., division two random variables, Central limit theorem. Relations among sample distributions. Some inequalities for binomial random variable, approximations of Poisson distribution, relations Poisson, binomial and F-distributions. Calculation algorithms for binomial, geometrical and Poisson distributions. Parameter estimations, average, sample variance, unbiased estimation, unbiased sample variance, bias of sample standard deviation, distributions of average and sample variance ? large sample, small sample. Parameter estimation, some use of order statistics. Order statistics, distribution of i-th order statistic, minimum and maximum distribution, symmetrical distribution, quantiles, sample median, parameters of uniform distribution estimation, Shifted exponential distribution. Parameter estimation, consistency, method of moments, maximum likelihood, MLE estimation for normal, exponential and uniform, sufficient statistic. Interval estimation. Parameter interval estimation, idea, vague of reliability interval, reliability interval symmetrical in probability, symmetrical in location, intuitive method for reliability interval construction. Tests of hypotheses. Simple hypotheses, simple alternative, type I. and II errors, its influence, rejection region, test power, most powerful and uniformly powerful test, Neyman-Pearson lemma, parameter tests, power function, exponential family testing, likelihood ratio tests. Tests of hypotheses, sequential tests, Wald?s tests, sequential tests about parameters, random count sums distribution, Wald?s tests properties in contrary classical tests. n-dimensional distribution, estimation, test and dependencyy models, two-dimensional normal distribution, detailed analysis, correlation, sample correlation, Fisher transformation, correlation interval estimation, independence (non-correlation) hypothesis. Non-parametrical tests, categorical variables distribution, goodness-of-fit test, modification, homogeneity test.

Learning activities and teaching methods
Lecture supplemented with a discussion, Lecture with practical applications, One-to-One tutorial
  • Contact hours - 56 hours per semester
  • Preparation for formative assessments (2-20) - 30 hours per semester
  • Preparation for an examination (30-60) - 60 hours per semester
prerequisite
professional knowledge
Basic knowledge in probability theory and statistics are expected.
formulovat a vysvětlit definici pravděpodobnosti (v rozsahu předmětu KMA/PSA)
popsat a vysvětlit základní operace maticového počtu (v rozsahu předmětu KMA/LA)
popsat a vysvětlit základní pojmy diferenciálního a integrálního počtu (v rozsahu předmětů KMA/M1 a KMA/M2)
professional skills
odlišovat různé typy náhodných veličin (diskrétní, spojité) a různé typy rozdělení
využívat znalostí základních statistických metod a postupů pro jednoduchou analýzu dat
general eligibility
N/A
learning outcomes
professional knowledge
to understanding the basic statistical problems
professional skills
to identify methods suitable for solving real problems.
general eligibility
N/A
teaching methods
professional knowledge
Lecture supplemented with a discussion
One-to-One tutorial
Lecture with practical applications
assessment methods
Combined exam
professional skills
Combined exam
general eligibility
Combined exam
Recommended literature
  • http://en.wikipedia.org/wiki/Probability_distribution.
  • Hátle, Jaroslav. Základy počtu pravděpodobnosti a matematické statistiky. Praha : SNTL, 1972.
  • Rao, Radhakrishna Calyampudi. Lineární metody statistické indukce a jejich aplikace. Praha : Academia, 1978.
  • Reif, J. Metody matematické statistiky. Plzeň : Západočeská univerzita, 2004. ISBN 80-7043-302-7.
  • Rényi, Alfréd. Teorie pravděpodobnosti. 1. české vyd. Praha : Academia, 1972.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Applied Sciences Information Systems (2016) Informatics courses 3 Winter
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 3 Winter
Faculty of Applied Sciences Information Systems (2014) Informatics courses 3 Winter
Faculty of Applied Sciences Information Systems (2017) Informatics courses 3 Winter
Faculty of Applied Sciences Geomatics (2016) Construction industry, geodesy and cartography 3 Winter
Faculty of Applied Sciences Geomatics (2015) Construction industry, geodesy and cartography 3 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2015) Mathematics courses 3 Winter
Faculty of Applied Sciences Information Systems (2015) Informatics courses 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2007) Economy 3 Winter
Faculty of Applied Sciences Training Teachers of Mathematics at Higher Secondary Scholls (2014) Pedagogy, teacher training and social care 2 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2011) Mathematics courses 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2017) Economy 3 Winter
Faculty of Applied Sciences Geomatics (2014) Construction industry, geodesy and cartography 3 Winter
Faculty of Applied Sciences Mathematics and Management (2011) Mathematics courses 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (1) Economy 3 Winter
Faculty of Applied Sciences Geomatics (2017) Construction industry, geodesy and cartography 3 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 3 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2017) Mathematics courses 3 Winter
Faculty of Applied Sciences Information Systems (1) Informatics courses 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2016) Economy 3 Winter
Faculty of Applied Sciences General Mathematics (2012) Mathematics courses 3 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2017) Economy 3 Winter
Faculty of Applied Sciences Financial Informatics and Statistics (2016) Economy 3 Winter
Faculty of Applied Sciences Information Systems (2012) Informatics courses 3 Winter
Faculty of Applied Sciences Mathematics for Business Studies (2016) Mathematics courses 3 Winter