You have two envelopes with money, one has double the amount of the other. You pick one and see it has $100. Should you switch?

You have two envelopes with money, one has double the amount of the other. You pick one and see it has $100. Should you switch?

Approach: Calculate conditional expected value of other envelope given you observed $100.

Depends on prior distribution of money. If prior is improper uniform, expected value of switching is 1.25*$100, suggesting switch. But this leads to paradox. With proper prior, no benefit to switching.

Follow-up: What if you don't open the envelope?

Key concepts: conditional expectation, paradox, prior distribution.