Example: The Two Envelope Problem

• You are offered a choice between two envelopes. Each contains an unstated amount of cash and you are told that one of them contains twice as much as the other.

• You pick one of them, open it and find $x. This means that the other envelope has either $x/2 or $2x.

• You are now offered the choice of :

  • Keeping what you have: $x
    or
  • Exchanging it for the other (unopened);
    expected value:
    

• Should you switch?

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