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Relationship between two random variables having same expectation

  1. Jul 15, 2010 #1
    1. The problem statement, all variables and given/known data

    Say, it is known that
    [tex]E_X[f(X)] = E_X[g(X)] = a[/tex] where [tex]f(X)[/tex] and [tex]g(X)[/tex] are two functions of the same random variable [tex]X[/tex]. What is the relationship between [tex]f(X)[/tex] and [tex]g(X)[/tex]?

    2. Relevant equations



    3. The attempt at a solution

    My answer is [tex]f(X) = g(X) + h(X)[/tex] where [tex]E_X[h(X)] = 0[/tex].

    This relationship is apparent by taking expectation in both sides. But, is it necessarily and sufficiently true?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Jul 18, 2010 #2
    Anyone please?
     
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