Probability and Mathematical Statistics

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. Probability-random 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. Log-normal distribution.

7. Two-dimensional 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 two-sample 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. Probability-random 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. Log-normal distribution.

7. Two-dimensional 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 two-sample 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, ISBN-13:978-0-538-73352-6

Note:

Time-table for winter semester 2024/2025:

Time-table is not available yet

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: