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Equivalent probabilties

  1. Mar 30, 2007 #1
    1. The problem statement, all variables and given/known data
    Given a probability space, how do I find the family of all equivalent probabilities on the space?

    For example,
    let the discrete random variable X have uniform probability equal to 1/3, taking values 10, 2, and -3. the r.v. is represented on the finite probability space = {1, 2, 3}. How do I find the family of all equivalent probabilties?

    2. Relevant equations

    3. The attempt at a solution
    my thought would be should I be using the Radon-Nikodym Theorem? (which I honestly am not so familiar with). Or is the solution far simpler than that.

    All I ask is a direction or hint to work on first. thanks!
  2. jcsd
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