# Homework Help: Relationship between two random variables having same expectation

1. Jul 15, 2010

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. The attempt at a solution

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

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. Jul 18, 2010