272027.0 Probability Theory, Part 2 (5 cr)
Cooperation network course
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)
Grading scale:
0-5
Description
1) grunddragen i den axiomatiska uppbyggnaden av sannolikhetsteorin (sannolikhetsmått, sigma-algebra),
2) egenskaper hos flerdimensionella sannolikhetsfördelningar (speciellt normalfördelning),
3) sannolikhetsteoretiska olikheter (Markovs olikhet, Tjebysevs olikhet),
4) momentgenererande funktioner,
5) bevis för de stora talens lag (konvergens i sannolikhet) och den centrala gränsvärdessatsen samt deras tillämpningar i statistik
Learning outcomes
Efter genomgången kurs bör deltagaren
- förstå den matematiska definitionen av sannolikhet
- kunna räkna med sannolikheter
- förstå de stora talens lag och den centrala gränsvärdessatsen och deras bevis