Description:

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

Contents:

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.

Seminar contents:

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.

Recommended literature:

Jay L. Devore: Probability and statistics for engineering and the sciences. Duxbury, ISBN-13:978-0-538-73352-6

Keywords:

Mathematical statistics. Probability. Statistical methods.

Abbreviations used:

Semester:

• W ... winter semester (usually October - February)
• S ... spring semester (usually March - June)
• W,S ... both semesters

Mode of completion of the course:

• A ... Assessment (no grade is given to this course but credits are awarded. You will receive only P (Passed) of F (Failed) and number of credits)
• GA ... Graded Assessment (a grade is awarded for this course)
• EX ... Examination (a grade is awarded for this course)
• A, EX ... Examination (the award of Assessment is a precondition for taking the Examination in the given subject, a grade is awarded for this course)

Weekly load (hours per week):

• P ... lecture
• C ... seminar
• L ... laboratory
• R ... proseminar
• S ... seminar