SP2170 Doing Science Bayesian Solution of the Envelope Paradox Wayne M. Lawton Department of Mathematics National University of Singapore 2 Science Drive 2 Singapore 117543 Email matwml@nus.edu.sg http://www.math.nus.edu.sg/~matwml/courses/Undergraduate/SPS_Doing/2006/ Tel (65) 6516-2749 1

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

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