Credits: 5
Schedule: 07.01.2019 - 18.02.2019
Contact information for the course (applies in this implementation):
Lecturer: Kalle Kytölä
Teaching assistant: Niko Lietzén
Teaching Period (valid 01.08.2018-31.07.2020):
III Spring (2018-2019, 2019-2020)
Learning Outcomes (valid 01.08.2018-31.07.2020):
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
Content (valid 01.08.2018-31.07.2020):
- 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
Details on the course content (applies in this implementation):
Course contents
- Random numbers, vectors, and sequences
- Integration with respect to a probability measure
- Stochastic independence and product measure
- Law of large numbers and the central limit theorem
- (Conditional expectation with respect to a sigma-algebra)
Assessment Methods and Criteria (valid 01.08.2018-31.07.2020):
Weekly exercises and exam.
Elaboration of the evaluation criteria and methods, and acquainting students with the evaluation (applies in this implementation):
Grading
Exercises: There are 6 problem sets during the course, one each week. Written solutions are turned in for grading.
Quizzes: Before each lecture there is an online quiz in MyCourses.
Exam: The exam consists of 4 problems, to be completed in 3 hours.
Grade: The course grade is determined by whichever of the following scores is higher
- 100% exam score
- 50% exam score + 10% score of quizzes + 40% homework solutions
Workload (valid 01.08.2018-31.07.2020):
2 x 2h lectures, 1 x 2h exercises sessions
Study Material (valid 01.08.2018-31.07.2020):
J. Jacod & P. Protter: Probability Essentials. Universitext, Springer, 2004.
Details on the course materials (applies in this implementation):
The course follows lecture notes provided on the MyCourses page.
Substitutes for Courses (valid 01.08.2018-31.07.2020):
Mat-1.3601
Course Homepage (valid 01.08.2018-31.07.2020):
https://mycourses.aalto.fi/course/search.php?search=MS-E1600
Prerequisites (valid 01.08.2018-31.07.2020):
Familiarity with continuous functions and open sets (e.g. MS-C1540 Euklidiset avaruudet)
Grading Scale (valid 01.08.2018-31.07.2020):
0-5
- Teacher: Kytölä Kalle
- Teacher: Lietzén Niko