Course Details
Mathematics 4
Academic Year 2024/25
BAA004 course is part of 9 study plans
BPC-SI / S Winter Semester 3rd year
BPC-SI / K Winter Semester 3rd year
BPC-SI / E Winter Semester 3rd year
BPC-SI / M Winter Semester 3rd year
BPC-SI / V Winter Semester 3rd year
BPC-MI Winter Semester 2nd year
BPC-EVB Winter Semester 3rd year
BKC-SI Winter Semester 3rd year
BPA-SI Winter Semester 3rd year
Course Guarantor
Institute
Language of instruction
Czech, English
Credits
5 credits
Semester
winter
Forms and criteria of assessment
course-unit credit and examination
Offered to foreign students
To offer to students of all faculties
Course on BUT site
Lecture
13 weeks, 2 hours/week, elective
Syllabus
- Continuous and discrete random variable (vector), probability function, density function. Probability.
- Properties of probability. Cumulative distribution and its properties.
- Relationships between probability, density and cumulative distributions. Marginal random vector. Independent random variables.
- Numeric characteristics of random variables: mean and variance, standard deviation, variation coefficient, modus, quantiles. Rules of calculation mean and variance.
- Numeric characteristics of random vectors: covariance, correlation coefficient, covariance and correlation matrices.
- Some discrete distributions - discrete uniform, alternative, binomial, Poisson, hypergeometric - definition, using.
- Some continuous distributions - continuous uniform, exponential, normal, multivariate normal - definition applications.
- Chi-square distribution, Student´s distribution - definition, using. Random sampling, sample statistics.
- Distribution of sample statistics. Point estimation of distribution parameters, desirable properties of an estimator.
- Confidence interval for distribution parameters.
- Fundamentals of hypothesis testing. Tests of hypotheses for normal distribution parameters. Asymptotic test on the alternative distribution parameter.
- Goodness-of-fit tests. Chi - square test. Basics of regression analysis.
- Linear model.
Exercise
13 weeks, 2 hours/week, compulsory
Syllabus
- Empirical probability and density distributions. Histogram.
- Probability and density distributions. Probability.
- Cumulative distribution. Relationships between probability, density and cumulative distributions.
- Transformation of random variable.
- Marginal and simultaneous random vector. Independence of random variables.
- Calculation of mean, variance, standard deviation, variation coefficient, modus and quantiles of a random variable. Calculation rules of mean and variance.
- Correlation coefficient. Test.
- Calculation of probability in some cases of discrete probability distributions - alternative, binomial, Poisson, hypergeometric.
- Calculation of probability for normal distribution. Work with statistical tables.
- Calculation of sample statistics. Application problems for their distribution.
- Confidence interval for normal distribution parameters.
- Tests of hypotheses for normal distribution parameters. Asymptotic test on the alternative distribution parameter.
- Goodness-of-fit test.