Mathematics 4B

The course is a substitute for:

Mathematics 4B (X01M4B)

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course covers probability, statistics and introduction to random processes for electronics and telecommunications. First classical probability is introduced, then theory of random variables is developed including examples of the most important types of discrete and continuous distributions. Next chapters contain transformations of random variables, expectation and variance, conditional distributions and correlation and independence of random variables. Statistical methods for point estimates, confidence intervals and testing hypotheses on parameters of normal distribution are investigated.

Requirements:

The requirement for receiving the credit is an active participation in the tutorials. The final grading reflects the performance in both the written and oral part of the examination the student sits for at the end of the course.

Syllabus of lectures:

1. Random phenomena, probability.

2. Conditional probability, statistical independence.

3. Random variables, distribution functions, quantiles, discrete and continuous random variables.

4. Expected value, variance, moments of random variables.

5. Transformation of random variables.

6. Several random variables, joint probability function, covariance and correlation.

7. Random sampling, sampling statistics.

8. Chebyshev inequality, central limit theorem.

9. Chi-square and Student disributions.

10. Point estimates, moment and maximum likelihood estimates.

11. Confidence intervals for normal and alternative distributions.

12. Testing hypotheses on expected value and variance.

13. Stochastic processes. Stationary processes, covariance function.

14. Ergodic processes, estimating covariance function.

Syllabus of tutorials:

1. Random phenomena, probability.

2. Conditional probability, statistical independence.

3. Random variables, distribution functions, quantiles, discrete and continuous random variables.

4. Expected value, variance, moments of random variables.

5. Transformation of random variables.

6. Several random variables, joint probability function, covariance and correlation.

7. Random sampling, sampling statistics.

8. Chebyshev inequality, central limit theorem.

9. Chi-square and Student disributions.

10. Point estimates, moment and maximum likelihood estimates.

11. Confidence intervals for normal and alternative distributions.

12. Testing hypotheses on expected value and variance.

13. Stochastic processes. Stationary processes, covariance function.

14. Ergodic processes, estimating covariance function.

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)