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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024
UPOZORNĚNÍ: Jsou dostupné studijní plány pro následující akademický rok.

Probability and Mathematical Statistics

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Code Completion Credits Range Language
D01PMS ZK 4P Czech
Garant předmětu:
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 2023/2024:
Time-table is not available yet
Time-table for summer semester 2023/2024:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-06-15
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