How did you get from one of these steps to the other? Shouldn’t the second be E[log((Y+d+d)/(Y+d))]?
Yeah, it should. Hmm. Also, looking at my derivation as a whole it’s implausible that E(d/X) ~ E(2d/Y) -- the second should be almost twice as big.
So I think I made a mistake there. I suspect that to get the result we need to use the approximation d/X ~ d/Y (roughly right since d is very small in comparison to Y).
Yeah, it should. Hmm. Also, looking at my derivation as a whole it’s implausible that E(d/X) ~ E(2d/Y) -- the second should be almost twice as big.
So I think I made a mistake there. I suspect that to get the result we need to use the approximation d/X ~ d/Y (roughly right since d is very small in comparison to Y).