Mathematics 4A

The course is a substitute for:

Probability and Statistics (X01M4A)

Lecturer:

Tutor:

Supervisor:

Department of Mathematics

Synopsis:

The course covers probability and basic statistics for power engineering. 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 moment generating functions and moments of random variables, expectation and variance, conditional distributions and correlation and independence of random variables. Statistical methods for point estimates and confidence intervals 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 event.

2. Probability of a random event.

3. Conditional probability, Bayes's theorem.

4. Repeated independent trials, Bernoulli experiment.

5. Random variable; distribution of random variable.

6. Cummulative distribution function, density function and probability function.

7. Expected value and variance.

8. Moment generating function, moments of random variable.

9. Important types of random variables.

10. Random vector and its characterization.

11. Marginal and conditional distributions.

12. Correlation and independence of random variables.

13. Random sampling and sample statistics.

14. Point estimates and confidence intervals.

Syllabus of tutorials:

1. Random event.

2. Probability of a random event.

3. Conditional probability, Bayes's theorem.

4. Repeated independent trials, Bernoulli experiment.

5. Random variable; distribution of random variable.

6. Cummulative distribution function, density function and probability function.

7. Expected value and variance.

8. Moment generating function, moments of random variable.

9. Important types of random variables.

10. Random vector and its characterization.

11. Marginal and conditional distributions.

12. Correlation and independence of random variables.

13. Random sampling and sample statistics.

14. Point estimates and confidence intervals.

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:

• Heavy-current Engineering- structured studies (compulsory elective course)