Mathematics 4B

Prerequisite:

Mathematics 2 (X01MA2)

Grading of the course requires grading of the following courses:

Introduction to Algebra (X01ALG)
Mathematics 1 (X01MA1)

Lecturer:

Jaroslav Tišer, Anna Něničková

Tutor:

Jaroslav Tišer, Anna Něničková

Supervisor:

Department of Mathematics

Synopsis:

The course is focused on basic elements of probability theory and statistics. Basic probability structure (probability space, random variables, random vectors) is introduced. The exposition ulminates in central limit theorem. Probability theory is then applied to statistical methods (interval estimations, testing tatistical hypotheses).

Requirements:

The requirement for receiving the credit is an active participation in the tutorials.

Syllabus of lectures:

1. Structure of random events and probability

2. Types of probability spaces

3. Conditional probability. Bayes formula

4. Random variable (distribution function, moments)

5. Independence of random variables

6. Transformations of random variables

7. Random vector, covariance and correlations of random variables

8. Central limit theorem

9. Random choice and basic statistics

10.Basic statistical distributions (Chi, Student)

11. Poit estimates of statistical parametrs

12. Interval estimates of parameters of gaussian and alternative distributions.

13. Testing statistical hypotheses

14. Basic concepts of the theory of random processes

Syllabus of tutorials:

1. Structure of random events and probability

2. Types of probability spaces

3. Conditional probability. Bayes formula

4. Random variable (distribution function, moments)

5. Independence of random variables

6. Transformations of random variables

7. Random vector, covariance and correlations of random variables

8. Central limit theorem

9. Random choice and basic statistics

10.Basic statistical distributions (Chi, Student)

11. Poit estimates of statistical parametrs

12. Interval estimates of parameters of gaussian and alternative distributions.

13. Testing statistical hypotheses

14. Basic concepts of the theory of random processes

Study Objective:

Study materials:

1. M. K. Ochi: Applied Probability & Stochastic Processes In Engineering. Wiley 1989.

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Electronics and Communication Technology - structured studies (compulsory elective course)