Probability and Mathematical Statistics
Code  Completion  Credits  Range  Language 

D01PMS  ZK  4P  Czech 
 Course guarantor:
 Daniela Jarušková
 Lecturer:
 Daniela Jarušková
 Tutor:
 Supervisor:
 Department of Mathematics
 Synopsis:

Introduction to probability and statistics with applications, combinatorics, random variables, probability distributions (with
emphasis to distributions used in hydrology), Bayesian inference, inferential statistics, estimation of parameters, hypothesis
testing, and linear regression.
 Requirements:
 Syllabus of lectures:

1. Basic descriptive statistics. Inferential statistics.
2. Probabilityrandom events, definition of probability, condition probability, independence of random events.
3. Discrete random variables & distribution, expectation, variance, examples of discrete distributions.
4. Continuous random variables & density, distribution functions, quantiles, expectation, variance, examples of continuous
distributions.
5. Normal distribution.
6. Lognormal distribution.
7. Twodimensional distribution, marginal distribution, independence, correlation.
8. Central limit theorem. Distribution of mean.
9. Estimation of parameters. Properties of estimators. Confidence intervals.
10. Hypotheses testing. Principle of hypotheses testing. One and twosample problems.
11. Linear regression. Method of least squares.
12. Linear regression. Estimation of parameters. Prediction.
 Syllabus of tutorials:

1. Basic descriptive statistics. Inferential statistics.
2. Probabilityrandom events, definition of probability, condition probability, independence of random events.
3. Discrete random variables & distribution, expectation, variance, examples of discrete distributions.
4. Continuous random variables & density, distribution functions, quantiles, expectation, variance, examples of continuous
distributions.
5. Normal distribution.
6. Lognormal distribution.
7. Twodimensional distribution, marginal distribution, independence, correlation.
8. Central limit theorem. Distribution of mean.
9. Estimation of parameters. Properties of estimators. Confidence intervals.
10. Hypotheses testing. Principle of hypotheses testing. One and twosample problems.
11. Linear regression. Method of least squares.
12. Linear regression. Estimation of parameters. Prediction.
 Study Objective:

Basic knowledge of inferential statistics.
 Study materials:

Jay L. Devore: Probability and statistics for engineering and the sciences. Duxbury, ISBN13:9780538733526
 Note:
 Timetable for winter semester 2024/2025:
 Timetable is not available yet
 Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans: