[miloshh]

You just painstakingly carried out the absolute analysis, which I know works.

Let X be the value in the envelope you have, and Y in the other one (X and Y are both random variables with well-known distributions). Then E[Y/X] = 1.25. That's what I wanted you to explain. You just keep saying that E[X] = E[Y], which I know.

Note that this paradox would not arise if X and Y were independent, since then E[Y/X] = E[Y] / E[X] = 1.

[scotty79]

What reasoning leads to claim that E[Y/X] = 1.25 ?

It can't be the reasoning from wikipedia about two envelopes problem because it has error in steps 4 and 5 so results in step 7 and further are nonsensical.

I painstakingly shown how this reasoning should look like to be right and that in fact E[Y/X] = E[Y] / E[X] = 1