Probability and Statistics

Kód předmětu: 101MPRS
Garant předmětu: prof. RNDr. Daniela Jarušková, CSc.
Zakončení předmětu: ZK
Počet kreditů: 4 kred.
Rozsah výuky: 2+2

Anotace(semestr B232)
The goal is to get a basic knowledge in probability and inferential statistics. Probability. Discrete and continuous random variables. Normal distribution. Asymptotic distribution of a mean. Multivariate distribution. Independence and correlation. Parameter estimation. Hypothesis testing. Simple linear regression.
Obsah 
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.

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.

Literatura 
Povinná literatura:
[1]  Jay L. Devore: Probability and statistics for engineering and the sciences. Duxbury, ISBN-13:978-0-538-73352-6
Návaznosti 
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Studijní plány 
Předmět je zařazen do následujících studijních plánů:

- studijní plán Civil Engineering (BD2020), skupina Civil Engineering, Optional subjects, 7-8th semester (BD20200700_2), dop. semestr 8 (valid from 2020/21 to 2022/23 )
- studijní plán Civil Engineering (BD2023), skupina Civil Engineering, Optional subjects, 7-8th semester (BD20230700_2), dop. semestr 8 (valid from 2023/24 )