# Stochastic Modelling and Processing

## Code

IT-SMP1

## Version

1.1

## Offered by

ICT Engineering

## ECTS

5### Prerequisites

Upper level mathematics equivalent to A-levels. Calculus.

### Main purpose

### Knowledge

- The main working tools and concepts of stochastic modelling
- Probability theory and distributions
- Inferential statistics

### Skills

- 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
- Account for the processing of random signals in linear systems
- Calculate and interpret auto- and cross-correlation functions for random signals
- Calculate and interpret power density spectra and coherence functions
- Calculates and estimate errors and uncertainties.

### Competences

- 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
- Auto- and cross-correlation functions and correlation coefficients
- Power density spectra and coherence functions
- Analysis of errors in experiments
- Design of statistical experiments
- Creating hypotheses and confidence intervals
- Presentation of statistical data
- Linear and exponential regression
- Analysis of variance

### Teaching methods and study activities

### Resources

*Applied Statistics and Probability for Engineers*, 4th edition Wiley (obtained from library)

*Probabilistic Methods of Signal and System Analysis*, 3rd edition. Oxford University Press (electronic version will be made available).

### Evaluation

### Examination

The final exam is a 3 hour written exam and takes place at Campus Horsens. Supplementary materials and aids are allowed. 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.

### Grading criteria

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.

### Additional information

### Responsible

Richard Brooks

### Valid from

8/1/2016 12:00:00 AM

### Course type

6. semester

7. semester

Electives

### Keywords

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