Please note! Course description is confirmed for two academic years, which means that in general, e.g. Learning outcomes, assessment methods and key content stays unchanged. However, via course syllabus, it is possible to specify or change the course execution in each realization of the course, such as how the contact sessions are organized, assessment methods weighted or materials used.
LEARNING OUTCOMES
After completing the course, the participant
- Can compute the expected value of a random number as an integral with respect to a probability measure
- Can compute probabilities related to independent random variables by using a product measure
- Recognizes different types of convergence of a random sequence
- Can explain how and when a random sum can be approximated by a Gaussian distribution
- Can represent conditional probabilities with respect to the information content of a sigma-algebra
Credits: 5
Schedule: 11.01.2021 - 22.02.2021
Teacher in charge (valid 01.08.2020-31.07.2022): Lasse Leskelä
Teacher in charge (applies in this implementation):
Contact information for the course (applies in this implementation):
CEFR level (applies in this implementation):
Language of instruction and studies (valid 01.08.2020-31.07.2022):
Teaching language: English
Languages of study attainment: English
CONTENT, ASSESSMENT AND WORKLOAD
Content
Valid 01.08.2020-31.07.2022:
- Random numbers, vectors, and sequences
- Describing information using sigma-algebras
- Integration with respect to a probability measure
- Stochastic independence and product measure
- Law of large numbers and the central limit theorem
Assessment Methods and Criteria
Valid 01.08.2020-31.07.2022:
Weekly exercises and exam.
Applies in this implementation:
Grading
The course grade g is determined by normalized exam points (e = E/Emax), normalized homework points (h = H/Hmax), and normalized quiz points (q = Q/Qmax)
according tog = f( max( 1.00*e, 0.50*e + 0.40*h + 0.10*q ) )
where f: [0,1] → {0,1,2,3,4,5} is a deterministic increasing function such that f(0.5) ≥ 1 and f(0.9) ≥ 5.
Workload
Valid 01.08.2020-31.07.2022:
2 x 2h lectures, 1 x 2h exercise sessions with weekly homeworks
DETAILS
Study Material
Valid 01.08.2020-31.07.2022:
K Kytölä. Probability theory. Lecture notes. Aalto University 2019.
Applies in this implementation:
Extensive stochastics "bible":
- Olav Kallenberg: Foundations of Modern Probability. Springer 2002.
Finnish reading material:
- Tommi Sottinen: Todennäköisyysteoria. 2006. http://lipas.uwasa.fi/~tsottine/lecture_notes/tnt.pdf
- Olav Kallenberg: Foundations of Modern Probability. Springer 2002.
Substitutes for Courses
Valid 01.08.2020-31.07.2022:
Mat-1.3601
Prerequisites
Valid 01.08.2020-31.07.2022:
Familiarity with number sequences and series, continuous functions, and open sets (e.g. MS-C1540 Euklidiset avaruudet)
- Teacher: Evdoridis Stavros
- Teacher: Karjalainen Joona
- Teacher: Leskelä Lasse
- Teacher: Radnell David