Probability and Statistics

Course guarantor:

Lecturer:

Tutor:

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:

Subject can be adapted according to students demands.

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Water and Environmental Engineering (compulsory elective course)
• Water and Environmental Engineering (compulsory elective course)
• Water and Environmental Engineering (PS)