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# Stochastic Modelling and Processing

IT-SMP1

1.2

ICT Engineering

## ECTS

5

### Prerequisites

Upper level mathematics equivalent to A-levels. Calculus.

### Main purpose

The ubiquitous presence of uncertainty and noise in the engineering sciences makes it mandatory to understand and quantify random phenomena. To achieve this goal the course will provide a solid introduction to the theory of stochastic processes. Special attention is given to applications and the student will model and analyse complex stochastic situations as encountered in practice. The applications include examples from various engineering fields such as information technologies and communications, signal processing, and more.

### Knowledge

After successfully completing the course, the student will have gained knowledge about:
• The main working tools and concepts of stochastic modelling
• Probability theory and distributions
• Confidence Intervals and Hypothesis Testing
• Inferential statistics

### Skills

After successfully completing the course, the student will be able to:
• Apply results from basic probability theory including conditional probability
• Use probability density and distributions functions of one and two variables
• Account for random variables and random processes
• Calculate and estimate errors and uncertainties.

### Competences

After successfully completing the course, the student will have acquired competencies in:
• Planning experiments and state hypothesis
• Presenting statistical results from experiments
• Modelling experimental data with regression
• Analysing experimental results and test hypotheses

### Topics

• Experiments and the concepts of probability
• Calculations of probability
• Often encountered probability density and distribution functions
• Random variables and random processes
• Analysis of errors in experiments
• Design of statistical experiments
• Creating hypotheses and confidence intervals
• Presentation of statistical data
• Linear and exponential regression

### Teaching methods and study activities

Approximately 150 hours. The course is a mixture of lectures, problem solving and computer/laboratory exercises with approximately 1/3 of the time devoted to each part.

### Resources

Python 3.X
Montgomery, D.C. & Runger, G.C. Applied Statistics and Probability for Engineers, 4th edition Wiley (obtained from library)
Montgomery, D.C. & Runger, G.C. Applied Statistics and Probability for Engineers, 7th edition Wiley (e-book)

### Evaluation

Grading will be done according to the 7-scale, using an internal examiner.

### Examination

​The final exam is a 3 hour written exam and takes place at Campus Horsens. All supplementary materials and aids are allowed, e.g. using a computer as a reference work.
Communication of any sort is not allowed during the exam and will lead to
expulsion of all involved parties from the exam.

The re-exam may be held as an oral examination.

According to the 7-point grading scale, interrnal examiner.

Mark 12:
Awarded to students who have shown excellent comprehension of the above-mentioned competences. A few minor errors and shortfalls are acceptable.

Mark 02:
Awarded to students for the just acceptable level of comprehension of the required competences.

Richard Brooks

### Valid from

8/8/2019 12:00:00 AM

6. semester
7. semester
Electives

### Keywords

Experiments and the concepts of probability, mathematical models based on random variation