Probability and Statistics
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. 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. 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. Twosample 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, ISBN13:9780538733526
 Note:
 Timetable for winter semester 2024/2025:

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  Timetable for summer semester 2024/2025:
 Timetable is not available yet
 The course is a part of the following study plans: