I have a problem for the past few weeks and couldn't find the answer in the books or in the internet. I know that in general:

E(g(X1, X2, ...)) is not equal to g(E(x1), E(X2) ,...) where E() is the expectation operator and g() is a function. For example E(XY) is not equal to E(X)E(Y) and we are tolerating an error of Cov(XY) by this approximation. What is the error in general case I described above? I am forced to use such an approximation in a problem and I want to know how much error I am committing. I really appreciate your help and suggestions, I am really stuck!

Best Regards,

Mohammad