1. SP2170 Doing Science Bayesian Solution of the Envelope Paradox
Wayne M. Lawton
Department of Mathematics
National University of Singapore
2 Science Drive 2
Singapore
Tel (65) 1

2. Let n be the event: there are n dollars in an envelope, be the
event: my envelope has half the amount in the other and
the event: my envelope has twice the amount in the other, then
Baye’s Theorem 
and clearly

4. BAYESIAN SOLUTION
The expected value in your envelope is
The expected value in the other envelope is
where
and this gives the correct value
The envelope paradox arises by mistakenly setting
which gives the wrong value