Mathematics BSc
Course description
2013.
Borromean Rings
Probability theory 2
Hours
lect+pc		 Credits
lect+pc		 Assessment Specialization Course code
lect/pc		 Semester Status
2 + 2 2 + 3 exam +
term grade		 applied math. mm1c1vs5a
mm1c2vs5a		 5 alternative
Strong Weak Prerequisites
Practice class
Strong:
Probability theory1L-m (mm1c1vs3m) or
Probability theory1L-a (mm1c1vs3a)
Strong:
Analysis4L-p (mm1c1an4m) or
Analysis4L-a (mm1c1an4a)
Lecture
Weak:
practice class
Remarks
  • Both pure and applied mathematics students can choose whether to take the applied or pure mathematics version of Probability theory 2 (it is compulsory to take one of these two courses). The pure mathematics version covers more material.
Syllabus designed by:
Literature
    Recommended:
    • A. A. Borovkov: Probability Theory. Springer, 2013.
    • W. Feller: An Introduction to Probability Theory and Its Applications. Vol. 2, 2nd edition, Wiley, 1971.
    • A. N. Shiryaev: Probability. 2nd edition, Springer, 1995.
    Syllabus
    • Kolmogorov’s probability field. Random variables, distribution, expectation, variance.
    • Independence.
    • Convergence in probability, in Lp, a.s. and weak convergence. Uniform integrability.
    • Prohorov’s theorem.
    • Characteristic function, the central limit theorem.
    • Martingales, stopping times. Maximal inequalities, convergence theorems.
    • Strong laws of large numbers.
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