Advertisement

Elementary Probability Theory

  • Albert N. Shiryaev
Chapter
Part of the Problem Books in Mathematics book series (PBM)

Abstract

Verify the following relations involving the operations ∩ (intersection) and ∪(union): AB = BA, AB = BA (commutativity), A ∪(BC) = (AB) ∪C, A ∩ (BC) = (AB) ∩ C (associativity),A ∩ (BC) = (AB) ∪(AC), A ∪(BC) = (AB) ∩ (AC) (distributivity), AA = A, AA = A (idempotent property of ∩ and ∪).

References

  1. 6.
    Berger, M.A.: An Introduction to Probability and Stochastic Processes. Springer, New York (1993)MATHGoogle Scholar
  2. 12.
    Bolshev, L.N., Smirnov, N.V.: Tablicy matematicheskoĭ statistiki. Nauka (Science), Moscow (1983)Google Scholar
  3. 39.
    Feller, W.: An Introduction to Probability Theory and Its Applications, vols. I and II, 3rd edn. Wiley, New York (1968)Google Scholar
  4. 40.
    Fristedt, B., Gray, L.: A Modern Approach to Probability Theory. Birkhäuser, Boston (1997)MATHGoogle Scholar
  5. 62.
    Khrennikov, A.: Interpretations of Probability. VSP, Utrecht (1999)MATHGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Albert N. Shiryaev
    • 1
    • 2
  1. 1.Department of Probability TheoryM.V. Lomonosov Moscow State UniveristyMoscowRussia
  2. 2.V.A. Steklov Institute of MathematicsRussian Academy of SciencesMoscowRussia

Personalised recommendations