RNDr. Helena Koutková, CSc.

Institute of Mathematics and Descriptive Geometry

Student will be able to solve simple practical probability problems and use basic statistical methods for interval estimates, testing parametric and non-parametric statistical hypotheses and linear models.

Basic knowledge of the theory of one and more functions (derivative, partial derivative, limit and continuous functions, graphs of functions). Ability to calculate definite integrals, double and triple integrals and knowledge of their basic applications.

Not required.

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations - lectures, seminars.

Students will receive credit based on attendance in practise classes and passing of a written test with at least 50% score. A written exam with a pass score of at least 50% will follow. The exam will last 90 minutes. It will consist of three practical (calculations) tasks and one task with theoretical questions.

The students should get an overview of teh basic properties of probability to be able to deal with simple practical problems in probability. They should get familiar with the basic statistical methods used for interval estimates, testing statistical hypotheses, and linear model.

Vymezení kontrolované výuky a způsob jejího provádění stanoví každoročně aktualizovaná vyhláška garanta předmětu.

2 hours/week, 13 weeks, elective

1. Continuous and discrete random variable (vector), probability function, density function. Probability.
2. Properties of probability. Cumulative distribution and its properties.
3. Relationships between probability, density and cumulative distributions. Marginal random vector.
4. Independent random variables. Numeric characteristics of random variables: mean and variance, standard deviation, variation coefficient, modus, quantiles. Rules of calculation mean and variance.
5. Numeric characteristics of random vectors: covariance, correlation coefficient, covariance and correlation matrices.
6. Some discrete distributions - discrete uniform, alternative, binomial, Poisson - definition, using.
7. Some continuous distributions - continuous uniform, exponential, normal, multivariate normal - definition applications.
8. Chi-square distribution, Student´s distribution - definition, using. Random sampling, sample statistics.
9. Distribution of sample statistics. Point estimation of distribution parameters, desirable properties of an estimator.
10. Confidence interval for distribution parameters.
11. Fundamentals of hypothesis testing. Tests of hypotheses for normal distribution parameters.
12. Goodness-of-fit tests. Chi - square test. Basics of regression analysis.
13. Linear model.

2 hours/week, 13 weeks, compulsory

1. Empirical probability and density distributions. Histogram.
2. Probability and density distributions. Probability.
3. Cumulative distribution. Relationships between probability, density and cumulative distributions.
4. Transformation of random variable.
5. Marginal and simultaneous random vector. Independence of random variables.
6. Calculation of mean, variance, standard deviation, variation coefficient, modus and quantiles of a random variable. Calculation rules of mean and variance.
7. Correlation coefficient. Test.
8. Calculation of probability in some cases of discrete probability distributions - alternative, binomial, Poisson.
9. Calculation of probability for normal distribution. Work with statistical tables.
10. Calculation of sample statistics. Application problems for their distribution.
11. Confidence interval for normal distribution parameters.
12. Tests of hypotheses for normal distribution parameters.
13. Goodness-of-fit test.