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Main menu for Browse IS/STAG
Course info
KMA / SA1
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Course description
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Department/Unit / Abbreviation
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KMA
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SA1
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Academic Year
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2024/2025
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Academic Year
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2024/2025
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Title
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Statistical Analysis 1
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
5
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
3
[Hours/Week]
Tutorial
1
[Hours/Week]
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Course credit prior to examination
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No
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Course credit prior to examination
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No
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Automatic acceptance of credit before examination
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No
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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Automatic acceptance of credit before examination
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No
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Summer semester
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0 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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4 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Winter semester
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Semester taught
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Winter semester
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Minimum (B + C) students
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1
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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| No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
| Periodicity |
every year
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| Specification periodicity |
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Fundamental theoretical course |
No
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| Fundamental course |
No
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| Fundamental theoretical course |
No
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| Evaluation scale |
1|2|3|4 |
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Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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KMA/ASF, KMA/OBM
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The main goal of this course is to obtain abilities use of statistics to solve real problems.
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Requirements on student
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Knowledge and abilities assessed: All assessment tasks will assess the learning outcomes, especially, the ability to provide logical and coherent proofs of results, procedures and specific problems related to statistic inference.
Assessment criteria: The main criteria for marking will be clear and logical formulation of solution methods and correctness of obtained results.
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Content
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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.
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Preparation for formative assessments (2-20)
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30
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Contact hours
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56
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Preparation for an examination (30-60)
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60
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Total
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146
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
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| Basic knowledge in probability theory and statistics are expected. |
| describe and explain the basic operations of matrix calculus (within the scope of the KMA/LA subject) |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
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| identify different types of random variables (discrete, continuous) and different types of distribution |
| Use knowledge of basic statistical methods and procedures for simple data analysis. |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
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| N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
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| to understanding the basic statistical problems |
Skills - skills resulting from the course: |
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| to identify methods suitable for solving real problems. |
Competences - competences resulting from the course: |
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| N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
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| Combined exam |
Skills - skills achieved by taking this course are verified by the following means: |
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| Combined exam |
Competences - competence achieved by taking this course are verified by the following means: |
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| Combined exam |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
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| Lecture supplemented with a discussion |
| One-to-One tutorial |
| Interactive lecture |
| Project-based instruction |
Skills - the following training methods are used to achieve the required skills: |
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| Interactive lecture |
Competences - the following training methods are used to achieve the required competences: |
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| Project-based instruction |
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