The problem I'm having with this is that since the derivative of the e^X is just e^X and X is assumed to be a whole number as it didn't specify otherwise, this distribution should end up being the same for both Y and Y'.
Secondly, you tell us to assume that the conditional distribution of Y "satisfies the five attributes of classical regression." I'm not sure what you mean by "satisfies." It's already been stated that the distribution is symmetric so I couldn't say that the skewness attribute has been satisfied.
I may be looking at this problem all wrong, but I appreciate any input you may have.