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

Probability and Statistics

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Code Completion Credits Range Language
101MPSE Z,ZK 6 3P+2C English
Garant předmětu:
Daniela Jarušková
Lecturer:
Daniela Jarušková
Tutor:
Daniela Jarušková
Supervisor:
Department of Mathematics
Synopsis:

Inferential statistics. Theory of probability. Random variables and their characteristics. Parameter estimation. Theory of hypotheses testing. Linear regression.

Requirements:

Basic calculus.

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. Descriptive statistics. - Excel

2. Probability. Bayesian theorem.

3. Discrete distribution.

4. Normal distribution.

5. How to use Excel for getting different probabilities and quantiles.

6. Multiple distribution. Independence. Correlation.

7. Linear combination of normally distributed random variables.

8.Parameter estimation.

9. Two-sample test.

10. Linear regression.

11. Linear regression - prediction.

12. Monte Carlo method.

Study Objective:

Students should understand what inferential statistics brings to us and what is the role of theory of probability in it. They learn the most important statistical methods.

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:
06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue
Wed
Thu
Fri
roomTH:B-369

11:00–13:50
(lecture parallel1)
Thákurova 7 (budova FSv)
B369
roomTH:B-369

16:00–17:50
(lecture parallel1
parallel nr.103)

Thákurova 7 (budova FSv)
B369
roomTH:B-369

14:00–15:50
(lecture parallel1
parallel nr.102)

Thákurova 7 (budova FSv)
B369
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 2024-05-25
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