MATH3010 Probability Theory I (5 cr)
Cooperation network course
Network: Vaasa Higher Education Consortium
Network: Cross-institutional studies in advanced courses in mathematics and statistics
This course is offered through the Network for Advanced Studies in Mathematics. These studies are available for the following degree students:
- Bachelor's Degree Programme in Mathematics
- Master's Degree Programme in Mathematics
- Bachelor's Degree Programme in Mathematics (Subject Teacher)
- Master's Degree Programme in Mathematics (Subject Teacher)
- Bachelor's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Master's Degree Programme in Mathematics, Chemistry or Physics Subject Teacher Education and Primary Teacher Education (Specialication in Mathematics)
- Doctoral Programme in Mathematics and Statistics
- Doctoral Programme in Mathematics and Science (Specialication in Mathematics)
Description
Probability space, random vectors, expectation, independence, characteristic function, almost sure convergence, Lp-convergence, convergence in probability, weak convergence, laws of large numbers, central limit theorem
Learning outcomes
The student will have a deep understanding about the measure theoretical foundations of probability: sigma-algebras, extension theorems and independence. The student will have a deep understanding about the measure theoretic integral. The student will have a deep understanding about the major limit theorems of probability: laws of large numbers and the central limit theorem.
Description of prerequisites
Elementary courses in calculus, probability and statistics.