Probability and Statistics

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

Basics of probability theory, in particular conditional probability and Bayesian approach. Notions needed for statistics: Descriptions of random variables and vectors, laws of large numbers. Basics of mathematical statistics: Point and interval estimates, methods of parameters estimation and hypotheses testing. Basic notions and results of the theory of Markov chains.

Requirements:

Syllabus of lectures:

1. Basic notions of probability theory.

2. Random variables and their description.

3. Characteristics of random variables.

4. Random vector, independence, conditional probability, Bayes formula.

5. Operations with random variables, mixture of random variables.

6. Basic notions of statistics. Sample mean, sample variance.

7. Method of moments, method of maximum likelihood.

8. EM algorithm.

9. Interval estimates of mean and variance.

10. Hypotheses testing.

11. Goodness-of-fit tests, tests of correlation, non-parametic tests.

12. Applications in decision-making under uncertainty and pattern recognition. Least squares method.

13. Markov chains.

14. Classification of states of Markov chains. Overview of applications.

Syllabus of tutorials:

1. Elementary probability.

2. Random variables and their description.

3. Mean and variance of random variables.

4. Unary operations with random variables.

5. Random vector, joint distribution.

6. Binary operations with random variables.

7. Mixture of random variables.

8. Sample mean, sample variance.

9. Method of moments, method of maximum likelihood.

10. Interval estimates of mean and variance.

11. Hypotheses testing.

12. Least squares method.

13. Goodness-of-fit tests.

14. Markov chains, classification of states.

Study Objective:

Active participation at seminars and a fulfilled project - an ordinary statistical task trained at seminars, based on real data. Will be specified at seminars by tutors.

Study materials:

[1] Papoulis, A.: Probability and Statistics, Prentice-Hall, 1990.

[2] Mood, A.M., Graybill, F.A., Boes, D.C.: Introduction to the Theory of Statistics. 3rd ed., McGraw-Hill, 1974.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: