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Stochastic Modelling and Processes
Code
IT-SMP1
Version
3.0
Offered by
ICT Engineering
ECTS
5
Prerequisites
Students taking the course are expected to have basic mathematical skills (e.g. from IT-DMA1 or IT-MSE1).
There is a limit of 40 participants in the course. If more than 40 students select the course, we will select the 40 students based on their grades in IT-DMA1, IT-ADS1, and IT-ALI (if the student has had it) or other equivalent math courses.
Main purpose
This course introduces probability theory, focusing on the mathematical description of random systems. Students will explore the fundamental properties of random variables, including their mean, variance, and standard distributions commonly used in probability theory and statistics. The course also covers statistical hypothesis testing, with applications to various models, and an analysis of random models. Additionally, students will gain hands-on experience using Python for simulating random variables and conducting statistical tests.
Knowledge
Upon completing this course, students will have acquired foundational knowledge in probability theory and its applications. Specifically, they will be able to:
- Understand the core concepts of probability:
Students will demonstrate an understanding of experiments, sample spaces, and the fundamental properties of probability, such as independence and conditional probability, enabling them to approach random systems methodically.
- Describe random variables and their distributions:
Students will be able to define and explain random variables, and describe their key characteristics such as mean, variance, and standard distributions (e.g., normal, binomial, and Poisson distributions).
- Explain statistical hypothesis testing:
Students will gain knowledge of hypothesis testing principles and be able to apply statistical tests to various models. They will understand how to formulate null and alternative hypotheses, as well as analyse and interpret p-values and confidence intervals.
- Analyse random processes:
Students will explore random processes, such as Markov Chains, and understand their applications in modelling systems that evolve over time.
- Utilise Python for data analysis:
Through hands-on experience, students will acquire the knowledge to use Python programming for working with random variables, conducting statistical tests, and visualizing statistical data.
Skills
Upon completing this course, students will have acquired foundational knowledge in probability theory and its applications. Specifically, they will be able to:
- Understand the core concepts of probability:
Students will demonstrate an understanding of experiments, sample spaces, and the fundamental properties of probability, such as independence and conditional probability, enabling them to approach random systems methodically.
- Describe random variables and their distributions:
Students will be able to define and explain random variables, and describe their key characteristics such as mean, variance, and standard distributions (e.g., normal, binomial, and Poisson distributions).
- Explain statistical hypothesis testing:
Students will gain knowledge of hypothesis testing principles and be able to apply statistical tests to various models. They will understand how to formulate null and alternative hypotheses, as well as analyse and interpret p-values and confidence intervals.
- Analyse random processes:
Students will explore random processes, such as Markov Chains, and understand their applications in modelling systems that evolve over time.
- Utilise Python for data analysis:
Through hands-on experience, students will acquire the knowledge to use Python programming for working with random variables, conducting statistical tests, and visualizing statistical data.
Competences
Upon completing this course, students will have gained the competence to:
- Develop and implement probabilistic models:
Students will be able to design and apply probabilistic models to real-world problems, adapting existing methods or developing new approaches to solve complex tasks in various domains, such as social sciences, engineering, and finance.
- Critically evaluate statistical results and models:
Students will have the competence to assess the quality of statistical models and the accuracy of data analysis results. They will be able to critique experimental designs, identify potential sources of error, and propose improvements to ensure more reliable conclusions.
- Integrate programming skills for advanced data analysis:
Students will be able to independently use Python for data analysis, conducting statistical tests, and applying models like Markov Chains. They will integrate their programming skills to explore and analyse datasets effectively in various professional and academic contexts.
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
Creating hypotheses and confidence intervals
Presentation of statistical data
Linear regression
Markov Chains
Python programming
Teaching methods and study activities
The mode of teaching will be classroom based and will involve lectures by the teacher and going through exercises in class.
The students are also expected to work on exercises before classes.
The total workload for the student is expected be around 130 hours.
Resources
Python 3.X
Montgomery, D.C. & Runger, G.C. Applied Statistics and Probability for Engineers, 4th edition Wiley
Montgomery, D.C. & Runger, G.C. Applied Statistics and Probability for Engineers, 7th edition Wiley (e-book)
Evaluation
Examination
Exam prerequisites:
None
Exam type:
The exam has two parts:
- The first part is a Flowlock exam in Wiseflow.
- The second part is a Wiseflow exam without Flowlock.
The second part must be completed in the Jupyter Notebook environment and the answers must be submitted in Wiseflow.
Part 1 has a duration of 3 hours and part 2 has a duration of 1 hour. The exam has a total duration of 4 hours.
The student will not be able to access the second part before the first part is concluded.
Part 1 weighs 75% and Part 2 weighs 25% in the final grade.
Tools allowed:
In the first part the students are allowed to use any notes, books, and/or other written/printed material and will have access to pdf files on their laptop.
The students may bring their own calculator.
In the second part all supplementary materials and aids are allowed, e.g., using a computer as a reference work.
It is not allowed, however, to use AI-tools such as CoPilot, ChatGPT, Bing, etc.
Communication of any sort is not allowed during the exam and will lead to expulsion of all involved parties from the exam.
Re-exam:
Re-exams may be oral.
Grading criteria
Grading based on the Danish 7-point scale.
Additional information
Responsible
Richard Brooks (rib)
Valid from
2/1/2025 12:00:00 AM
Course type
6. semester
7. semester
Elective for the specialization Data Engineering
Electives
Web 6 og 7
Keywords
random variables, independence, mean, variance, estimation, confidence intervals, hypothesis testing, Markov chains, the Python packages