Statistical Methods in MathematicsLaajuus (3 ECTS)

Objective

After completing the course the student will understand the statistical nature of numerical data and will know the basic concepts in data handling. The student will know the basic concepts and methods related to estimation and testing. The student will understand statistical nature of a digital image.
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After completing the course the student will be able to carry out simple statistical tests, to estimate parameters, to analyse and process a digital image with histogram methods.

Content

1. Probability and conditional probability
2. Discrete and continuous distributions: e.g. binomial, exponential, Poisson, normal
3. Nature of data, data handling and processing in a computer
4. Statistical nature of data: estimation and testing
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Statistical methods in image processing
5. Histogram-processing
6. Correlation

Assessment criteria, satisfactory (1)

The student understands the concept of probability and is able to estimate probabilities of a practical trial. The student knows some basic concepts in combinatorics and statistics. The student can do simple statistical calculations to solve simple problems.

Assessment criteria, good (3)

In addition to having satisfactory knowledge in the topics of the course the student is able to identify and use some common distributions in a practical setting. The student understands the statistical nature of a practical measurement. The student can estimate uncertainties of measurements. The student has basic knowledge of doing simple tests.

Assessment criteria, excellent (5)

In addition to having good knowledge in the topics of the course the student is able to apply fluently different standard methods of statistics to solve engineering problems. The student is able to use the Central Limit Theorem in applications. The student knows how to approximate distributions by other distributions.