1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question about probability measure

  1. Sep 7, 2005 #1
    An probability measure on same space [itex]\Omega[/itex] is a function of subsets of [itex]\Omega[/itex] satisfying three axioms:

    (i) For every set [itex]A \subset \Omega[/itex], the value of the function is a non-negative number: P(A) [itex]\geqslant[/itex] 0.

    (ii) For any two disjoint sets A and B, the value of the function for their union A + B is equal to the sum of its value for A and its value for B:

    P(A + B) = P(A) + P(B) provided A.B = [itex]{\O}[/itex].

    (iii) The value of the function for [itex]\Omega[/itex] (as a subset) is equal to 1:

    P([itex]\Omega[/itex]) = 1.

    Now, reply these questions:

    If M is a probability measure, show:

    (a) that the function M/2 satisfies Axiom(i) and (ii) but not (iii).

    (b) the function [itex]M^2[/itex] satisfies (i) and (iii) but not necessary (ii); give a counterexample to (ii).
  2. jcsd
  3. Sep 7, 2005 #2


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    We can't help if you if you haven't tried it.
  4. Sep 7, 2005 #3


    User Avatar
    Science Advisor

  5. Sep 8, 2005 #4
  6. Sep 8, 2005 #5


    User Avatar

    (Either it's that simple or i don't understand the problem)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?